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Bhowmik S, Ghosh A, Chandni U. Emergent phases in graphene flat bands. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:096401. [PMID: 39059412 DOI: 10.1088/1361-6633/ad67ed] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 07/26/2024] [Indexed: 07/28/2024]
Abstract
Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.
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Affiliation(s)
- Saisab Bhowmik
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
| | - Arindam Ghosh
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - U Chandni
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
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2
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Kinoshita K, Lin YC, Moriya R, Okazaki S, Onodera M, Zhang Y, Senga R, Watanabe K, Taniguchi T, Sasagawa T, Suenaga K, Machida T. Crossover between rigid and reconstructed moiré lattice in h-BN-encapsulated twisted bilayer WSe 2 with different twist angles. NANOSCALE 2024; 16:14358-14365. [PMID: 38953240 DOI: 10.1039/d4nr01863j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
A moiré lattice in a twisted-bilayer transition metal dichalcogenide (tBL-TMD) exhibits a complex atomic reconstruction effect when its twist angle is less than a few degrees. The influence of the atomic reconstruction on material properties of the tBL-TMD has been of particular interest. In this study, we performed scanning transmission electron microscopy (STEM) imaging of a moiré lattice in h-BN-encapsulated twisted bilayer WSe2 with various twist angles. Atomic-resolution imaging of the moiré lattice revealed a reconstructed moiré lattice below a crossover twist angle of ∼4° and a rigid moiré lattice above this angle. Our findings indicate that h-BN encapsulation has a considerable influence on lattice reconstruction, as the crossover twist angle was larger in h-BN-encapsulated devices compared to non-encapsulated devices. We believe that this difference is due to the improved flatness and uniformity of the twisted bilayers with h-BN encapsulation. Our results provide a foundation for a deeper understanding of the lattice reconstruction in twisted TMD materials with h-BN encapsulation.
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Affiliation(s)
- Kei Kinoshita
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Yung-Chang Lin
- National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba 305-8565, Japan
| | - Rai Moriya
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Shota Okazaki
- Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama, Kanagawa 226-8501, Japan
| | - Momoko Onodera
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Yijin Zhang
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Ryosuke Senga
- National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba 305-8565, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takao Sasagawa
- Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama, Kanagawa 226-8501, Japan
| | - Kazu Suenaga
- The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan
| | - Tomoki Machida
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan.
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3
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Chen S, Chaudhary S, Refael G, Lewandowski C. Enhancing shift current response via virtual multiband transitions. COMMUNICATIONS PHYSICS 2024; 7:250. [PMID: 39070108 PMCID: PMC11271335 DOI: 10.1038/s42005-024-01729-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 07/02/2024] [Indexed: 07/30/2024]
Abstract
Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The myriad of factors governing shift-current response, however, poses significant challenges in finding such strong shift-current materials. Here we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. We further relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Furthermore, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit an enhanced shift current response.
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Affiliation(s)
- Sihan Chen
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 USA
- Department of Physics, California Institute of Technology, Pasadena, CA 91125 USA
| | - Swati Chaudhary
- Department of Physics, The University of Texas at Austin, Austin, TX 78712 USA
- Department of Physics, Northeastern University, Boston, MA 02115 USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
| | - Gil Refael
- Department of Physics, California Institute of Technology, Pasadena, CA 91125 USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 USA
| | - Cyprian Lewandowski
- National High Magnetic Field Laboratory, Tallahassee, Florida, FL 32310 USA
- Department of Physics, Florida State University, Tallahassee, FL 32306 USA
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4
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Wang Y, Wang Z, Cao L, Han Y, Peng H, Wang Z, Xue Y, Watanabe K, Taniguchi T, Lu J, Duan J, Gao HJ, Jiang Y, Mao J. Local Gate Enhanced Correlated Phases in Twisted Monolayer-Bilayer Graphene. ACS NANO 2024; 18:17707-17714. [PMID: 38924709 DOI: 10.1021/acsnano.4c02733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/28/2024]
Abstract
Manipulating the flat band degeneracy and thus getting the correlated insulating phases has been an ideal thread for realizing the exotic quantum phenomenon in the moiré system. To achieve this goal, the delicately tuned twist angle and a substantial displacement field (D) are rigorously requested. Here, we report our scanning tunneling microscope (STM) work on reaching these correlated insulating states in twisted monolayer-bilayer graphene through a decorated tip. It acts as a local top gate, leading to an enhanced local D, and enables us to fully lift the 8-fold degeneracy of the flat bands. With the aid of this technique, we further expand the correlated insulating states into a more tolerant twist angle that is down to 0.92°. Moreover, the correlated insulating phases in the hole-doping regime are realized. Our tip decoration method allows us to integrate the STM study with the high displacement field for the correlated phases in the twisted moiré systems.
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Affiliation(s)
- Yingbo Wang
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhengwen Wang
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Lu Cao
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yingzhuo Han
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Huimin Peng
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Zhongrui Wang
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yucheng Xue
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Junxi Duan
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Hong-Jun Gao
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yuhang Jiang
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jinhai Mao
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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Chen M, Xie Y, Cheng B, Yang Z, Li XZ, Chen F, Li Q, Xie J, Watanabe K, Taniguchi T, He WY, Wu M, Liang SJ, Miao F. Selective and quasi-continuous switching of ferroelectric Chern insulator devices for neuromorphic computing. NATURE NANOTECHNOLOGY 2024; 19:962-969. [PMID: 38965346 DOI: 10.1038/s41565-024-01698-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 05/19/2024] [Indexed: 07/06/2024]
Abstract
Quantum materials exhibit dissipationless topological edge state transport with quantized Hall conductance, offering notable potential for fault-tolerant computing technologies. However, the development of topological edge state-based computing devices remains a challenge. Here we report the selective and quasi-continuous ferroelectric switching of topological Chern insulator devices, showcasing a proof-of-concept demonstration in noise-immune neuromorphic computing. We fabricate this ferroelectric Chern insulator device by encapsulating magic-angle twisted bilayer graphene with doubly aligned h-BN layers and observe the coexistence of the interfacial ferroelectricity and the topological Chern insulating states. The observed ferroelectricity exhibits an anisotropic dependence on the in-plane magnetic field. By tuning the amplitude of the gate voltage pulses, we achieve ferroelectric switching between any pair of Chern insulating states in the presence of a finite magnetic field, resulting in 1,280 ferroelectric states with distinguishable Hall resistance levels on a single device. Furthermore, we demonstrate deterministic switching between two arbitrary levels among the record-high number of ferroelectric states. This unique switching capability enables the implementation of a convolutional neural network resistant to external noise, utilizing the quantized Hall conductance levels of the Chern insulator device as weights. Our study provides a promising avenue towards the development of topological quantum neuromorphic computing, where functionality and performance can be drastically enhanced by topological quantum materials.
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Affiliation(s)
- Moyu Chen
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Yongqin Xie
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Bin Cheng
- Institute of Interdisciplinary Physical Sciences, School of Science, Nanjing University of Science and Technology, Nanjing, China.
| | - Zaizheng Yang
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Xin-Zhi Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Fanqiang Chen
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Qiao Li
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Jiao Xie
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Wen-Yu He
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Menghao Wu
- School of Physics and School of Chemistry, Institute of Theoretical Chemistry, Huazhong University of Science and Technology, Wuhan, China
| | - Shi-Jun Liang
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
| | - Feng Miao
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
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Singh K, Chew A, Herzog-Arbeitman J, Bernevig BA, Vafek O. Topological heavy fermions in magnetic field. Nat Commun 2024; 15:5257. [PMID: 38898060 PMCID: PMC11187166 DOI: 10.1038/s41467-024-49531-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 06/07/2024] [Indexed: 06/21/2024] Open
Abstract
The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method-based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.
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Affiliation(s)
- Keshav Singh
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
- Department of Physics, Florida State University, Tallahassee, FL, 32306, USA
| | - Aaron Chew
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | | | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018, Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Oskar Vafek
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA.
- Department of Physics, Florida State University, Tallahassee, FL, 32306, USA.
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7
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Kumar R, Srivastav SK, Roy U, Park J, Spånslätt C, Watanabe K, Taniguchi T, Gefen Y, Mirlin AD, Das A. Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet. Nat Commun 2024; 15:4998. [PMID: 38866830 PMCID: PMC11169481 DOI: 10.1038/s41467-024-49446-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2023] [Accepted: 06/05/2024] [Indexed: 06/14/2024] Open
Abstract
Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.
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Affiliation(s)
- Ravi Kumar
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | | | - Ujjal Roy
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Jinhong Park
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - Christian Spånslätt
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96, Göteborg, Sweden
| | - K Watanabe
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Alexander D Mirlin
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - Anindya Das
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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Han X, Liu Q, Wang Y, Niu R, Qu Z, Wang Z, Li Z, Han C, Watanabe K, Taniguchi T, Song Z, Liu J, Mao J, Han Z, Chittari BL, Jung J, Gan Z, Lu J. Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice. NANO LETTERS 2024; 24:6286-6295. [PMID: 38747346 DOI: 10.1021/acs.nanolett.4c00948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.
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Affiliation(s)
- Xiangyan Han
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qianling Liu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yijie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Niu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuangzhuang Qu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhiyu Wang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuoxian Li
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Chunrui Han
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Zhida Song
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
| | - Jinhai Mao
- School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zheng Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Optoelectronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Bheema Lingam Chittari
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul 02504, Korea
- Department of Smart Cities, University of Seoul, Seoul 02504, Korea
| | - Zizhao Gan
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
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9
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Hoke JC, Li Y, May-Mann J, Watanabe K, Taniguchi T, Bradlyn B, Hughes TL, Feldman BE. Uncovering the spin ordering in magic-angle graphene via edge state equilibration. Nat Commun 2024; 15:4321. [PMID: 38773076 PMCID: PMC11109299 DOI: 10.1038/s41467-024-48385-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 04/30/2024] [Indexed: 05/23/2024] Open
Abstract
The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.
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Affiliation(s)
- Jesse C Hoke
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Yifan Li
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Julian May-Mann
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Barry Bradlyn
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Benjamin E Feldman
- Department of Physics, Stanford University, Stanford, CA, 94305, USA.
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA.
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA.
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10
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Bigeard G, Cresti A. Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:325502. [PMID: 38670079 DOI: 10.1088/1361-648x/ad4431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Accepted: 04/26/2024] [Indexed: 04/28/2024]
Abstract
We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08∘. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.
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Affiliation(s)
- Gaëlle Bigeard
- Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, CROMA, 38000 Grenoble, France
| | - Alessandro Cresti
- Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, CROMA, 38000 Grenoble, France
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11
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Zhu X, Sun J, Feng S, Guo H. Moiré band renormalization due to lattice mismatch in bilayer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:315502. [PMID: 38663420 DOI: 10.1088/1361-648x/ad43a3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 04/25/2024] [Indexed: 05/08/2024]
Abstract
We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.
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Affiliation(s)
- Xingchuan Zhu
- Interdisciplinary Center for Fundamental and Frontier Sciences, Nanjing University of Science and Technology, Jiangyin, Jiangsu 214443, People's Republic of China
| | - Junsong Sun
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Huaiming Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
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12
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Graham AJ, Park H, Nguyen PV, Nunn J, Kandyba V, Cattelan M, Giampietri A, Barinov A, Watanabe K, Taniguchi T, Andreev A, Rudner M, Xu X, Wilson NR, Cobden DH. Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer. NANO LETTERS 2024; 24:5117-5124. [PMID: 38629940 DOI: 10.1021/acs.nanolett.3c04866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2024]
Abstract
Stacking monolayer semiconductors creates moiré patterns, leading to correlated and topological electronic phenomena, but measurements of the electronic structure underpinning these phenomena are scarce. Here, we investigate the properties of the conduction band in moiré heterobilayers of WS2/WSe2 using submicrometer angle-resolved photoemission spectroscopy with electrostatic gating. We find that at all twist angles the conduction band edge is the K-point valley of the WS2, with a band gap of 1.58 ± 0.03 eV. From the resolved conduction band dispersion, we deduce an effective mass of 0.15 ± 0.02 me. Additionally, we observe replicas of the conduction band displaced by reciprocal lattice vectors of the moiré superlattice. We argue that the replicas result from the moiré potential modifying the conduction band states rather than final-state diffraction. Interestingly, the replicas display an intensity pattern with reduced 3-fold symmetry, which we show implicates the pseudo vector potential associated with in-plane strain in moiré band formation.
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Affiliation(s)
- Abigail J Graham
- Department of Physics, University of Warwick, Coventry CV4 7AL, U.K
| | - Heonjoon Park
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Paul V Nguyen
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - James Nunn
- Department of Physics, University of Warwick, Coventry CV4 7AL, U.K
| | - Viktor Kandyba
- Elettra - Sincrotrone Trieste, S.C.p.A, Basovizza (TS), Friuli-Venezia Giulia 34149, Italy
| | - Mattia Cattelan
- Elettra - Sincrotrone Trieste, S.C.p.A, Basovizza (TS), Friuli-Venezia Giulia 34149, Italy
| | - Alessio Giampietri
- Elettra - Sincrotrone Trieste, S.C.p.A, Basovizza (TS), Friuli-Venezia Giulia 34149, Italy
| | - Alexei Barinov
- Elettra - Sincrotrone Trieste, S.C.p.A, Basovizza (TS), Friuli-Venezia Giulia 34149, Italy
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Anton Andreev
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Mark Rudner
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Xiaodong Xu
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
- Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Neil R Wilson
- Department of Physics, University of Warwick, Coventry CV4 7AL, U.K
| | - David H Cobden
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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13
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Hou Y, Zhou J, Xue M, Yu M, Han Y, Zhang Z, Lu Y. Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2024:e2311185. [PMID: 38616775 DOI: 10.1002/smll.202311185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Revised: 03/24/2024] [Indexed: 04/16/2024]
Abstract
The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".
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Affiliation(s)
- Yuan Hou
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Jingzhuo Zhou
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Minmin Xue
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Maolin Yu
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Ying Han
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Zhuhua Zhang
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Yang Lu
- Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, Hong Kong SAR, 999077, China
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14
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Zhou W, Ding J, Hua J, Zhang L, Watanabe K, Taniguchi T, Zhu W, Xu S. Layer-polarized ferromagnetism in rhombohedral multilayer graphene. Nat Commun 2024; 15:2597. [PMID: 38519502 PMCID: PMC10960043 DOI: 10.1038/s41467-024-46913-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 03/14/2024] [Indexed: 03/25/2024] Open
Abstract
Flat-band systems with strongly correlated electrons can exhibit a variety of phenomena, such as correlated insulating and topological states, unconventional superconductivity, and ferromagnetism. Rhombohedral multilayer graphene has recently emerged as a promising platform for investigating exotic quantum states due to its hosting of topologically protected surface flat bands at low energy, which have a layer-dependent energy dispersion. However, the complex relationship between the surface flat bands and the highly dispersive high-energy bands makes it difficult to study correlated surface states. In this study, we introduce moiré superlattices as a method to isolate the surface flat bands of rhombohedral multilayer graphene. The observed pronounced screening effects in the moiré potential-modulated rhombohedral multilayer graphene indicate that the two surface states are electronically decoupled. The flat bands that are isolated promote correlated surface states in areas that are distant from the charge neutrality points. Notably, we observe tunable layer-polarized ferromagnetism, which is evidenced by a hysteretic anomalous Hall effect. This is achieved by polarizing the surface states with finite displacement fields.
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Affiliation(s)
- Wenqiang Zhou
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
| | - Jing Ding
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
| | - Jiannan Hua
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
| | - Le Zhang
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Wei Zhu
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China.
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China.
| | - Shuigang Xu
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China.
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China.
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15
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Xin B, Zou K, Liu D, Li B, Dong H, Cheng Y, Liu H, Zou LJ, Luo F, Lu F, Wang WH. Electronic structures and quantum capacitance of twisted bilayer graphene with defects based on three-band tight-binding model. Phys Chem Chem Phys 2024; 26:9687-9696. [PMID: 38470341 DOI: 10.1039/d3cp05913h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
Twisted bilayer graphene (tBLG) with C vacancies would greatly improve the density of states (DOS) around the Fermi level (EF) and quantum capacitance; however, the single-band tight-binding model only considering pz orbitals cannot accurately capture the low-energy physics of tBLG with C vacancies. In this work, a three-band tight-binding model containing three p orbitals of C atoms is proposed to explore the modulation mechanism of C vacancies on the DOS and quantum capacitance of tBLG. We first obtain the hopping integral parameters of the three-band tight-binding model, and then explore the electronic structures and the quantum capacitance of tBLG at a twisting angle of θ = 1.47° under different C vacancy concentrations. The impurity states contributed by C atoms with dangling bonds located around the EF and the interlayer hopping interaction could induce band splitting of the impurity states. Therefore, compared with the quantum capacitance of pristine tBLG (∼18.82 μF cm-2) at zero bias, the quantum capacitance is improved to ∼172.76 μF cm-2 at zero bias, and the working window with relatively large quantum capacitance in the low-voltage range is broadened in tBLG with C vacancies due to the enhanced DOS around the EF. Moreover, the quantum capacitance of tBLG is further increased at zero bias with an increase of the C vacancy concentration induced by more impurity states. These findings not only provide a suitable multi-band tight-binding model to describe tBLG with C vacancies but also offer theoretical insight for designing electrode candidates for low-power consumption devices with improved quantum capacitance.
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Affiliation(s)
- Baojuan Xin
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Kaixin Zou
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Dayong Liu
- Department of Physics, School of Sciences, Nantong University, Nantong 226019, China
| | - Boyan Li
- National Institute of Clean-and-Low-Carbon Energy, and Beijing Engineering Research Center of Nano-structured Thin Film Solar Cells, Beijing 102211, China
| | - Hong Dong
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Yahui Cheng
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Hui Liu
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Liang-Jian Zou
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
| | - Feng Luo
- School of Materials Science and Engineering, Nankai University, Tianjin 300350, China
| | - Feng Lu
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
| | - Wei-Hua Wang
- Department of Electronic Science and Engineering, and Tianjin Key Laboratory of Efficient Utilization of Solar Energy, Nankai University, Tianjin 300350, China.
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16
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Chen Q, Zhang Z, Qin H, Bossart A, Yang Y, Chen H, Fleury R. Anomalous and Chern topological waves in hyperbolic networks. Nat Commun 2024; 15:2293. [PMID: 38480697 PMCID: PMC10937626 DOI: 10.1038/s41467-024-46551-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 03/01/2024] [Indexed: 03/17/2024] Open
Abstract
Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior.
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Affiliation(s)
- Qiaolu Chen
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Zhe Zhang
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Haoye Qin
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Aleksi Bossart
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Romain Fleury
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland.
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17
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Wang J, Cheng F, Sun Y, Xu H, Cao L. Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures. Phys Chem Chem Phys 2024; 26:7988-8012. [PMID: 38380525 DOI: 10.1039/d3cp04656g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.
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Affiliation(s)
- Jiamin Wang
- Changchun Institute of Optics, Fine Mechanics & Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, P. R. China.
- University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Fang Cheng
- State Key Laboratory for Organic Electronics and Information Displays & Jiangsu Key Laboratory for Biosensors, Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
| | - Yan Sun
- Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, P. R. China.
| | - Hai Xu
- Changchun Institute of Optics, Fine Mechanics & Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, P. R. China.
- University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, P. R. China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Liang Cao
- Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei 230031, P. R. China.
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18
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Szkudlarek A, Michalik JM, Serrano-Esparza I, Nováček Z, Novotná V, Ozga P, Kapusta C, De Teresa JM. Graphene removal by water-assisted focused electron-beam-induced etching - unveiling the dose and dwell time impact on the etch profile and topographical changes in SiO 2 substrates. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2024; 15:190-198. [PMID: 38352720 PMCID: PMC10862135 DOI: 10.3762/bjnano.15.18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/18/2024] [Indexed: 02/16/2024]
Abstract
Graphene is one of the most extensively studied 2D materials, exhibiting extraordinary mechanical and electronic properties. Although many years have passed since its discovery, manipulating single graphene layers is still challenging using standard resist-based lithography techniques. Recently, it has been shown that it is possible to etch graphene directly in water-assisted processes using the so-called focused electron-beam-induced etching (FEBIE), with a spatial resolution of ten nanometers. Nanopatterning graphene with such a method in one single step and without using a physical mask or resist is a very appealing approach. During the process, on top of graphene nanopatterning, we have found significant morphological changes induced in the SiO2 substrate even at low electron dose values (<8 nC/μm2). We demonstrate that graphene etching and topographical changes in SiO2 substrates can be controlled via electron beam parameters such as dwell time and dose.
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Affiliation(s)
- Aleksandra Szkudlarek
- Academic Centre for Materials and Nanotechnology, AGH University of Krakow, av. A. Mickiewicza 30, 30-059 Krakow, Poland
| | - Jan M Michalik
- Department of Solid State Physics, Faculty of Physics and Applied Computer Science, AGH University of Krakow, av. A. Mickiewicza 30, 30-059 Krakow, Poland
| | - Inés Serrano-Esparza
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Zdeněk Nováček
- NenoVision s.r.o. Purkyňova 649/127, 612 00 Brno, Czech Republic
| | - Veronika Novotná
- NenoVision s.r.o. Purkyňova 649/127, 612 00 Brno, Czech Republic
- Department of Power Electrical and Electronic Engineering, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3082/12, Královo Pole, 61600, Brno, Czech Republic
| | - Piotr Ozga
- Institute of Metallurgy and Materials Science, Polish Academy of Sciences, 25 Reymonta Street, 30-059 Krakow, Poland
| | - Czesław Kapusta
- Department of Solid State Physics, Faculty of Physics and Applied Computer Science, AGH University of Krakow, av. A. Mickiewicza 30, 30-059 Krakow, Poland
| | - José María De Teresa
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Laboratorio de Microscopías Avanzadas (LMA), Universidad de Zaragoza, E-50018 Zaragoza, Spain
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19
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Lu X, Xie B, Yang Y, Zhang Y, Kong X, Li J, Ding F, Wang ZJ, Liu J. Magic Momenta and Three-Dimensional Landau Levels from a Three-Dimensional Graphite Moiré Superlattice. PHYSICAL REVIEW LETTERS 2024; 132:056601. [PMID: 38364175 DOI: 10.1103/physrevlett.132.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Revised: 11/17/2023] [Accepted: 01/04/2024] [Indexed: 02/18/2024]
Abstract
In this Letter, we theoretically explore the physical properties of a new type of three-dimensional graphite moiré superlattice, the bulk alternating twisted graphite (ATG) system with homogeneous twist angle, which is grown by in situ chemical vapor decomposition method. Compared to twisted bilayer graphene (TBG), the bulk ATG system is bestowed with an additional wave vector degree of freedom due to the extra dimensionality. As a result, when the twist angle of bulk ATG is smaller than twice of the magic angle of TBG, there always exist "magic momenta" which host topological flat bands with vanishing in-plane Fermi velocities. Most saliently, when the twist angle is relatively large, a dispersionless three-dimensional zeroth Landau level would emerge in the bulk ATG, which may give rise to robust three-dimensional quantum Hall effects and unusual quantum-Hall physics over a large range of twist angles.
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Affiliation(s)
- Xin Lu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Bo Xie
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Yue Yang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Yiwen Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Xiao Kong
- Institute of Technology for Carbon Neutrality, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
- Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China
| | - Jun Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Feng Ding
- Institute of Technology for Carbon Neutrality, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
- Faculty of Materials Science and Energy Engineering, Shenzhen University of Advanced Technology, Shenzhen, China
| | - Zhu-Jun Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
- Liaoning Academy of Materials, Shenyang 110167, China
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20
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Pandey V, Mishra S, Maity N, Paul S, B AM, Roy AK, Glavin NR, Watanabe K, Taniguchi T, Singh AK, Kochat V. Probing Interlayer Interactions and Commensurate-Incommensurate Transition in Twisted Bilayer Graphene through Raman Spectroscopy. ACS NANO 2024. [PMID: 38295130 DOI: 10.1021/acsnano.3c08344] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Twisted 2D layered materials have garnered much attention recently as a class of 2D materials whose interlayer interactions and electronic properties are dictated by the relative rotation/twist angle between the adjacent layers. In this work, we explore a prototype of such a twisted 2D system, artificially stacked twisted bilayer graphene (TBLG), where we probe, using Raman spectroscopy, the changes in the interlayer interactions and electron-phonon scattering pathways as the twist angle is varied from 0° to 30°. The long-range Moiré potential of the superlattice gives rise to additional intravalley and intervalley scattering of the electrons in TBLG, which has been investigated through their Raman signatures. Density functional theory (DFT) calculations of the electronic band structure of the TBLG superlattices were found to be in agreement with the resonant Raman excitations across the van Hove singularities in the valence and conduction bands predicted for TBLG due to hybridization of bands from the two layers. We also observe that the relative rotation between the graphene layers has a marked influence on the second order overtone and combination Raman modes signaling a commensurate-incommensurate transition in TBLG as the twist angle increases. This serves as a convenient and rapid characterization tool to determine the degree of commensurability in TBLG systems.
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Affiliation(s)
- Vineet Pandey
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Subhendu Mishra
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Nikhilesh Maity
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Sourav Paul
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Abhijith M B
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Ajit K Roy
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States
| | - Nicholas R Glavin
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Abhishek K Singh
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Vidya Kochat
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
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21
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Scheer MG, Lian B. Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands. PHYSICAL REVIEW LETTERS 2023; 131:266501. [PMID: 38215385 DOI: 10.1103/physrevlett.131.266501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 11/10/2023] [Indexed: 01/14/2024]
Abstract
Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of m∼100 meV. We show that twisted bilayer graphene in which one or both layers have Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle θ≈0.7° and Dirac mass m≈100 meV. When both layers have Kekulé-O order, there is a large parameter regime around θ≈1° and m≳100 meV in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases of matter.
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Affiliation(s)
- Michael G Scheer
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Biao Lian
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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22
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Wu F, Xu Q, Wang Q, Chu Y, Li L, Tang J, Liu J, Tian J, Ji Y, Liu L, Yuan Y, Huang Z, Zhao J, Zan X, Watanabe K, Taniguchi T, Shi D, Gu G, Xu Y, Xian L, Yang W, Du L, Zhang G. Giant Correlated Gap and Possible Room-Temperature Correlated States in Twisted Bilayer MoS_{2}. PHYSICAL REVIEW LETTERS 2023; 131:256201. [PMID: 38181343 DOI: 10.1103/physrevlett.131.256201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 08/21/2023] [Accepted: 11/21/2023] [Indexed: 01/07/2024]
Abstract
Moiré superlattices have emerged as an exciting condensed-matter quantum simulator for exploring the exotic physics of strong electronic correlations. Notable progress has been witnessed, but such correlated states are achievable usually at low temperatures. Here, we report evidence of possible room-temperature correlated electronic states and layer-hybridized SU(4) model simulator in AB-stacked MoS_{2} homobilayer moiré superlattices. Correlated insulating states at moiré band filling factors v=1, 2, 3 are unambiguously established in twisted bilayer MoS_{2}. Remarkably, the correlated electronic state at v=1 shows a giant correlated gap of ∼126 meV and may persist up to a record-high critical temperature over 285 K. The realization of a possible room-temperature correlated state with a large correlated gap in twisted bilayer MoS_{2} can be understood as the cooperation effects of the stacking-specific atomic reconstruction and the resonantly enhanced interlayer hybridization, which largely amplify the moiré superlattice effects on electronic correlations. Furthermore, extreme large nonlinear Hall responses up to room temperature are uncovered near correlated electronic states, demonstrating the quantum geometry of moiré flat conduction band.
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Affiliation(s)
- Fanfan Wu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiaoling Xu
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China
| | - Qinqin Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yanbang Chu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Lu Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jian Tang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jieying Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jinpeng Tian
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yiru Ji
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Le Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yalong Yuan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhiheng Huang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jiaojiao Zhao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiaozhou Zan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Dongxia Shi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Gangxu Gu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yang Xu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Lede Xian
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Wei Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Luojun Du
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Guangyu Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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23
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Lu H, Long R, Fang WH. Electron- versus Spin-Phonon Coupling Governs the Temperature-Dependent Carrier Dynamics in the Topological Insulator Bi 2Te 3. J Am Chem Soc 2023; 145:25887-25893. [PMID: 37966512 DOI: 10.1021/jacs.3c10561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Ultrafast charge and spin dynamics have immense effects on the applications of topological insulators (TIs). By performing spin-adiabatic nonadiabatic molecular dynamics simulations in the presence of electron-phonon (e-ph) and spin-phonon couplings, we investigate temperature-dependent intra- and interband charge and spin relaxation dynamics via the bulk and surface paths in the three-dimensional TI Bi2Te3. The e-ph coupling dominates charge relaxation in the bulk path, and the relaxation rate is positively correlated with temperature due to the large energy gaps and weak spin polarization. Conversely, the relaxation dynamics exhibits an opposite temperature dependence in the surface path because of electron re-excitation and spin mismatching induced by spin-phonon coupling, which arises from small energy gaps and strong spin polarization. The two mechanisms rationalize the charge carriers being long-lived in the bulk and surface phases at low and room temperature, respectively. Additionally, strong thermal fluctuations of the topological states' magnetic moments destroy the spin-momentum locking and trigger backscattering at room temperature.
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Affiliation(s)
- Haoran Lu
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Wei-Hai Fang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, People's Republic of China
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24
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He M, Cai J, Zhang YH, Liu Y, Li Y, Taniguchi T, Watanabe K, Cobden DH, Yankowitz M, Xu X. Symmetry-Broken Chern Insulators in Twisted Double Bilayer Graphene. NANO LETTERS 2023. [PMID: 37983529 DOI: 10.1021/acs.nanolett.3c03414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
Twisted double bilayer graphene (tDBG) has emerged as a rich platform for studying strongly correlated and topological states, as its flat bands can be continuously tuned by both a perpendicular displacement field and a twist angle. Here, we construct a phase diagram representing the correlated and topological states as a function of these parameters, based on measurements of over a dozen tDBG devices encompassing two distinct stacking configurations. We find a hierarchy of symmetry-broken states that emerge sequentially as the twist angle approaches an apparent optimal value of θ ≈ 1.34°. Nearby this angle, we discover a symmetry-broken Chern insulator (SBCI) state associated with a band filling of 7/2 as well as an incipient SBCI state associated with 11/3 filling. We further observe an anomalous Hall effect at zero field in all samples supporting SBCI states, indicating spontaneous time-reversal symmetry breaking and possible moiré unit cell enlargement at zero magnetic field.
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Affiliation(s)
- Minhao He
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Jiaqi Cai
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Ya-Hui Zhang
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Yang Liu
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Yuhao Li
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - David H Cobden
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Matthew Yankowitz
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
- Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Xiaodong Xu
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
- Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
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25
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Christos M, Sachdev S, Scheurer MS. Nodal band-off-diagonal superconductivity in twisted graphene superlattices. Nat Commun 2023; 14:7134. [PMID: 37932262 PMCID: PMC10628137 DOI: 10.1038/s41467-023-42471-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 10/11/2023] [Indexed: 11/08/2023] Open
Abstract
The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.
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Affiliation(s)
- Maine Christos
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Mathias S Scheurer
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, A-6020, Austria.
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany.
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26
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Wang S, Song J, Sun M, Cao S. Emerging Characteristics and Properties of Moiré Materials. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2881. [PMID: 37947726 PMCID: PMC10649551 DOI: 10.3390/nano13212881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Revised: 10/26/2023] [Accepted: 10/29/2023] [Indexed: 11/12/2023]
Abstract
In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.
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Affiliation(s)
- Shaofeng Wang
- School of Physics, Liaoning University, Shenyang 110036, China
| | - Jizhe Song
- School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
| | - Mengtao Sun
- School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
| | - Shuo Cao
- School of Physics, Liaoning University, Shenyang 110036, China
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27
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Hu H, Rai G, Crippa L, Herzog-Arbeitman J, Călugăru D, Wehling T, Sangiovanni G, Valentí R, Tsvelik AM, Bernevig BA. Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:166501. [PMID: 37925696 DOI: 10.1103/physrevlett.131.166501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 09/11/2023] [Indexed: 11/07/2023]
Abstract
We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings ν=0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu et al., Phys. Rev. Lett. 131, 026502 (2023).PRLTAO0031-900710.1103/PhysRevLett.131.026502, Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.047601] and find the ordered states to have lower energy at ν=0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2 K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling ν=±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C_{3z}-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C_{3z} symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.
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Affiliation(s)
- Haoyu Hu
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
| | - Gautam Rai
- I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany
| | - Lorenzo Crippa
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | | | - Dumitru Călugăru
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Tim Wehling
- I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Giorgio Sangiovanni
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Roser Valentí
- Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - Alexei M Tsvelik
- Division of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
| | - B Andrei Bernevig
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- IKERBASQUE, Basque Foundation for Science, Bilbao 48009, Spain
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28
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Wu B, Zheng H, Li S, Wang CT, Ding J, He J, Liu Z, Wang JT, Liu Y. Enhanced Homogeneity of Moiré Superlattices in Double-Bilayer WSe 2 Homostructure. ACS APPLIED MATERIALS & INTERFACES 2023; 15:48475-48484. [PMID: 37796741 DOI: 10.1021/acsami.3c06949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/07/2023]
Abstract
Moiré superlattices have emerged as a promising platform for investigating and designing optically generated excitonic properties. The electronic band structure of these systems can be qualitatively modulated by interactions between the top and bottom layers, leading to the emergence of new quantum phenomena. However, the inhomogeneities present in atomically thin bilayer moiré superlattices created by artificial stacking have hindered a deeper understanding of strongly correlated electron properties. In this work, we report the fabrication of homogeneous moiré superlattices with controllable twist angles using a 2L-WSe2/2L-WSe2 homostructure. By adding extra layers, we provide additional degrees of freedom to tune the optical properties of the moiré superlattices while mitigating the nonuniformity problem. The presence of an additional bottom layer acts as a buffer, reducing the inhomogeneity of the moiré superlattice, while the encapsulation effect of the additional top and bottom WSe2 monolayers further enhances the localized moiré excitons. Our observations of alternating circularly polarized photoluminescence confirm the existence of moiré excitons, and their characteristics were further confirmed by theoretical calculations. These findings provide a fundamental basis for studying moiré potential correlated quantum phenomena and pave the way for their application in quantum optical devices.
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Affiliation(s)
- Biao Wu
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
- State Key Laboratory of High-Performance Complex Manufacturing, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
| | - Haihong Zheng
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
- State Key Laboratory of High-Performance Complex Manufacturing, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
| | - Shaofei Li
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
| | - Chang-Tian Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Junnan Ding
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
| | - Jun He
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
| | - Zongwen Liu
- School of Chemical and Biomolecular Engineering, The University of Sydney, Sydney, NSW 2006, Australia
- The University of Sydney Nano Institute, The University of Sydney, Sydney, NSW 2006 ,Australia
| | - Jian-Tao Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, People's Republic of China
| | - Yanping Liu
- School of Physics and Electronics, Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
- State Key Laboratory of High-Performance Complex Manufacturing, Central South University, 932 South Lushan Road, Changsha, Hunan 410083, People's Republic of China
- Shenzhen Research Institute of Central South University, Shenzhen 518000, People's Republic of China
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29
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Kim D, Pandey J, Jeong J, Cho W, Lee S, Cho S, Yang H. Phase Engineering of 2D Materials. Chem Rev 2023; 123:11230-11268. [PMID: 37589590 DOI: 10.1021/acs.chemrev.3c00132] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.
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Affiliation(s)
- Dohyun Kim
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Juhi Pandey
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Juyeong Jeong
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Woohyun Cho
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Seungyeon Lee
- Division of Chemical Engineering and Materials Science, Graduate Program in System Health Science and Engineering, Ewha Womans University, Seoul 03760, Korea
| | - Suyeon Cho
- Division of Chemical Engineering and Materials Science, Graduate Program in System Health Science and Engineering, Ewha Womans University, Seoul 03760, Korea
| | - Heejun Yang
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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30
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Zhang H, Shi Z, Jiang Z, Yang M, Zhang J, Meng Z, Hu T, Liu F, Cheng L, Xie Y, Zhuang J, Feng H, Hao W, Shen D, Du Y. Topological Flat Bands in 2D Breathing-Kagome Lattice Nb 3 TeCl 7. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2301790. [PMID: 37497878 DOI: 10.1002/adma.202301790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Revised: 06/18/2023] [Indexed: 07/28/2023]
Abstract
Flat bands (FBs) can appear in two-dimensional (2D) geometrically frustrated systems caused by quantum destructive interference (QDI). However, the scarcity of pure 2D frustrated crystal structures in natural materials makes FBs hard to be identified, let alone modulate FBs relating to electronic properties. Here, the experimental evidence of the complete electronic QDI induced FB contributed by the 2D breathing-kagome layers of Nb atoms in Nb3 TeCl7 (NTC) is reported. An identical chemical state and 2D localization characteristics of the Nb breathing-kagome layers are experimentally confirmed, based on which NTC is demonstrated to be a superior concrete candidate for the breathing-kagome tight-binding model. Furthermore, it theoretically establishes the tunable roles of the on-site energy over Nb sites on bandwidth, energy position, and topology of FBs in NTC. This work opens an aveanue to manipulate FB characteristics in these 4d transition-metal-based breathing-kagome materials.
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Affiliation(s)
- Hongrun Zhang
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Zhijian Shi
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Zhicheng Jiang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, P. R. China
| | - Ming Yang
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Jingwei Zhang
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Ziyuan Meng
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Tonghua Hu
- School of Physics, Beihang University, Beijing, 100191, P. R. China
| | - Fucai Liu
- School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P. R. China
| | - Long Cheng
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
- Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing, 100191, P. R. China
| | - Yong Xie
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Key Laboratory of Intelligent Systems and Equipment Electromagnetic Environment Effect, School of Electronic and Information Engineering, Beihang University, Beijing, 100191, P. R. China
| | - Jincheng Zhuang
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Haifeng Feng
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Weichang Hao
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
| | - Dawei Shen
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, P. R. China
- National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui, 230029, P. R. China
| | - Yi Du
- School of Physics, Beihang University, Beijing, 100191, P. R. China
- Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, P. R. China
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Cai J, Anderson E, Wang C, Zhang X, Liu X, Holtzmann W, Zhang Y, Fan F, Taniguchi T, Watanabe K, Ran Y, Cao T, Fu L, Xiao D, Yao W, Xu X. Signatures of fractional quantum anomalous Hall states in twisted MoTe 2. Nature 2023; 622:63-68. [PMID: 37315640 DOI: 10.1038/s41586-023-06289-w] [Citation(s) in RCA: 51] [Impact Index Per Article: 51.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2023] [Accepted: 06/06/2023] [Indexed: 06/16/2023]
Abstract
The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism1-3. In the presence of strong electron-electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge4-8. These states could host fractional excitations, including non-Abelian anyons-crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe2) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor10, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = -2/3 and v = -3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of [Formula: see text] and [Formula: see text], respectively. Moreover, the v = -1 state exhibits a dispersion corresponding to Chern number -1, consistent with the predicted QAH state11-14. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe2 moiré superlattices as a platform for exploring fractional excitations.
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Affiliation(s)
- Jiaqi Cai
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Eric Anderson
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Chong Wang
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Xiaowei Zhang
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Xiaoyu Liu
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | | | - Yinong Zhang
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Fengren Fan
- Department of Physics, University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, Hong Kong, China
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Ying Ran
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Ting Cao
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Di Xiao
- Department of Physics, University of Washington, Seattle, WA, USA
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Wang Yao
- Department of Physics, University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, Hong Kong, China
| | - Xiaodong Xu
- Department of Physics, University of Washington, Seattle, WA, USA.
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA.
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32
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Yuan Y, Liu P, Wu H, Chen H, Zheng W, Peng G, Zhu Z, Zhu M, Dai J, Qin S, Novoselov KS. Probing the Twist-Controlled Interlayer Coupling in Artificially Stacked Transition Metal Dichalcogenide Bilayers by Second-Harmonic Generation. ACS NANO 2023; 17:17897-17907. [PMID: 37698446 DOI: 10.1021/acsnano.3c03795] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/13/2023]
Abstract
Interlayer coupling plays a critical role in the electronic band structures and optoelectronic properties of van der Waals (vdW) materials and heterostructures. Here, we utilize optical second-harmonic generation (SHG) measurements to probe the twist-controlled interlayer coupling in artificially stacked WSe2/WSe2 homobilayers and WSe2/WS2 and WSe2/MoS2 heterobilayers with a postannealing procedure. In the large angle twisted WSe2/WSe2 and WSe2/WS2, the angular dependence of the SHG intensity follows the interference relations up to angles above 10°. For lower angles, the SHG is significantly suppressed. Furthermore, for the twisted WSe2/MoS2 the SHG intensity largely deviates from the coherent superposition model and shows consistent quenching for all the stacking angles. The suppressed SHG in twisted transition metal dichalcogenide (TMDC) bilayers is predominantly attributed to the interlayer coupling between the two adjacent monolayers. The evolution of the interlayer Raman mode in WSe2 demonstrates that the interlayer coupling in the twisted WSe2/WSe2 and WSe2/WS2 is highly angle-dependent. Alternatively, the interlayer coupling generally exists in the twisted WSe2/MoS2, regardless of the different angles. The interlayer coupling is further confirmed by the quenching and red-shift of the photoluminescence of WSe2 in the twisted TMDC bilayers. Combined with density functional theory calculations, we reveal that the stacking-angle-modulated interlayer coupling originates from the variation of the interlayer spacing and the binding energy in the twisted TMDC bilayers.
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Affiliation(s)
- Yuanjian Yuan
- College of Science & Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Peng Liu
- College of Science & Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Hongjian Wu
- College of Science & Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Haitao Chen
- College of Advanced Interdisciplinary Studies & Hunan Provincial Key Laboratory of Novel Nano-optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, Hunan 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Weihao Zheng
- College of Advanced Interdisciplinary Studies & Hunan Provincial Key Laboratory of Novel Nano-optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, Hunan 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Gang Peng
- College of Science & Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Zhihong Zhu
- College of Advanced Interdisciplinary Studies & Hunan Provincial Key Laboratory of Novel Nano-optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, Hunan 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Mengjian Zhu
- College of Advanced Interdisciplinary Studies & Hunan Provincial Key Laboratory of Novel Nano-optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, Hunan 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Jiayu Dai
- College of Science & Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Shiqiao Qin
- College of Advanced Interdisciplinary Studies & Hunan Provincial Key Laboratory of Novel Nano-optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, Hunan 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Kostya S Novoselov
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore 117544
- Department of Materials Science and Engineering, National University of Singapore, Singapore 117575
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33
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Datta A, Calderón MJ, Camjayi A, Bascones E. Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene. Nat Commun 2023; 14:5036. [PMID: 37596252 PMCID: PMC10439139 DOI: 10.1038/s41467-023-40754-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 08/07/2023] [Indexed: 08/20/2023] Open
Abstract
Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.
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Affiliation(s)
- Anushree Datta
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain
- Université Paris-Cité, CNRS, Laboratoire Matériaux et Phénomenes Quantiques, 75013, Paris, France
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - M J Calderón
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain
| | - A Camjayi
- Universidad de Buenos Aires, Ciclo Básico Común, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - E Bascones
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain.
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34
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Han X, Liu Q, Wang Y, Niu R, Qu Z, Wang Z, Li Z, Han C, Watanabe K, Taniguchi T, Song Z, Mao J, Han ZV, Gan Z, Lu J. Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene. NANO LETTERS 2023; 23:6875-6882. [PMID: 37466217 DOI: 10.1021/acs.nanolett.3c01262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2023]
Abstract
Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field (D) can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurement─a direct thermodynamic probe of Fermi surfaces─is highly demanding to be conducted under a constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronic states with isospin degeneracies of one and two can be identified. We also developed a method to measure the chemical potential at a fixed D, allowing for the extraction of energy variation during phase transitions. Furthermore, symmetry breaking could also be invoked in Landau levels, manifesting as quantum Hall ferromagnetism. Our work opens more opportunities for the thermodynamic characterization of displacement-field tuned van der Waals heterostructures.
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Affiliation(s)
- Xiangyan Han
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qianling Liu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yijie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Niu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuangzhuang Qu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhiyu Wang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuoxian Li
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Chunrui Han
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Zhida Song
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jinhai Mao
- School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zheng Vitto Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Optoelectronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Zizhao Gan
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
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35
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Nuckolls KP, Lee RL, Oh M, Wong D, Soejima T, Hong JP, Călugăru D, Herzog-Arbeitman J, Bernevig BA, Watanabe K, Taniguchi T, Regnault N, Zaletel MP, Yazdani A. Quantum textures of the many-body wavefunctions in magic-angle graphene. Nature 2023; 620:525-532. [PMID: 37587297 DOI: 10.1038/s41586-023-06226-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/16/2023] [Indexed: 08/18/2023]
Abstract
Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlated insulating1, unconventional superconducting2-5 and magnetic topological6-9 phases. The lack of microscopic information10,11 of possible broken symmetries has hampered our understanding of these phases12-17. Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order15, whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase12. Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements.
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Affiliation(s)
- Kevin P Nuckolls
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Ryan L Lee
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Myungchul Oh
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Dillon Wong
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Tomohiro Soejima
- Department of Physics, University of California, Berkeley, CA, USA
| | - Jung Pyo Hong
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Dumitru Călugăru
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Jonah Herzog-Arbeitman
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - B Andrei Bernevig
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
- Donostia International Physics Center, Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Nicolas Regnault
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA.
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36
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Walter AS, Zhu Z, Gächter M, Minguzzi J, Roschinski S, Sandholzer K, Viebahn K, Esslinger T. Quantization and its breakdown in a Hubbard-Thouless pump. NATURE PHYSICS 2023; 19:1471-1475. [PMID: 37841998 PMCID: PMC10567560 DOI: 10.1038/s41567-023-02145-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 06/23/2023] [Indexed: 10/17/2023]
Abstract
Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems1. For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue-the Thouless pump2-4. However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms5-9, the study of topological matter under variations in interparticle interactions has proven challenging10. Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump's robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter10, including edge effects11 and interaction-induced topological phases12-15.
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Affiliation(s)
- Anne-Sophie Walter
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Zijie Zhu
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Marius Gächter
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Joaquín Minguzzi
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Stephan Roschinski
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Kilian Sandholzer
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Konrad Viebahn
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
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37
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Hu H, Bernevig BA, Tsvelik AM. Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory. PHYSICAL REVIEW LETTERS 2023; 131:026502. [PMID: 37505959 DOI: 10.1103/physrevlett.131.026502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 06/13/2023] [Indexed: 07/30/2023]
Abstract
We apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.047601], to obtain its Kondo lattice limit. In this limit localized f electrons on a triangular lattice interact with topological conduction c electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0,±1,±2 are controlled by the heavy f electrons, while ν=±3 is at the border of a phase transition between two f-electron fillings. For ν=0,±1,±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the f moments in the full model and analytically prove the SU(4) Hund's rule for the ground state which maintains that two f electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite "bond-operators" method. We then compute the excitation spectrum of the f moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the f moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.
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Affiliation(s)
- Haoyu Hu
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
| | - B Andrei Bernevig
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Alexei M Tsvelik
- Division of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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38
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Yang C, Esin I, Lewandowski C, Refael G. Optical Control of Slow Topological Electrons in Moiré Systems. PHYSICAL REVIEW LETTERS 2023; 131:026901. [PMID: 37505954 DOI: 10.1103/physrevlett.131.026901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 05/17/2023] [Accepted: 06/13/2023] [Indexed: 07/30/2023]
Abstract
Floquet moiré materials possess optically-induced flat-electron bands with steady-states sensitive to drive parameters. Within this regime, we show that strong interaction screening and phonon bath coupling can overcome enhanced drive-induced heating. In twisted bilayer graphene (TBG) irradiated by a terahertz-frequency continuous circularly polarized laser, the extremely slow electronic states enable the drive to control the steady state occupation of high-Berry curvature electronic states. In particular, above a critical field amplitude, high-Berry-curvature states exhibit a slow regime where they decouple from acoustic phonons, allowing the drive to control the anomalous Hall response. Our work shows that the laser-induced control of topological and transport physics in Floquet TBG are measurable using experimentally available probes.
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Affiliation(s)
- Christopher Yang
- Department of Physics, IQIM, California Institute of Technology, Pasadena, California 91125, USA
| | - Iliya Esin
- Department of Physics, IQIM, California Institute of Technology, Pasadena, California 91125, USA
| | - Cyprian Lewandowski
- Department of Physics, IQIM, California Institute of Technology, Pasadena, California 91125, USA
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
- Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Gil Refael
- Department of Physics, IQIM, California Institute of Technology, Pasadena, California 91125, USA
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39
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Castro P, Shaffer D, Wu YM, Santos LH. Emergence of the Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model. PHYSICAL REVIEW LETTERS 2023; 131:026601. [PMID: 37505946 DOI: 10.1103/physrevlett.131.026601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 06/12/2023] [Indexed: 07/30/2023]
Abstract
While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density waves, and superconductivity. Importantly, we show that repulsive interactions can stabilize the long-sought pair-density-wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. This framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.
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Affiliation(s)
- Pedro Castro
- Department of Physics, Emory University, 400 Dowman Drive, Atlanta, Georgia 30322, USA
| | - Daniel Shaffer
- Department of Physics, Emory University, 400 Dowman Drive, Atlanta, Georgia 30322, USA
| | - Yi-Ming Wu
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - Luiz H Santos
- Department of Physics, Emory University, 400 Dowman Drive, Atlanta, Georgia 30322, USA
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40
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Bhowmik S, Ghawri B, Park Y, Lee D, Datta S, Soni R, Watanabe K, Taniguchi T, Ghosh A, Jung J, Chandni U. Spin-orbit coupling-enhanced valley ordering of malleable bands in twisted bilayer graphene on WSe 2. Nat Commun 2023; 14:4055. [PMID: 37422470 DOI: 10.1038/s41467-023-39855-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 06/26/2023] [Indexed: 07/10/2023] Open
Abstract
Recent experiments in magic-angle twisted bilayer graphene have revealed a wealth of novel electronic phases as a result of interaction-driven spin-valley flavour polarisation. In this work, we investigate correlated phases due to the combined effect of spin-orbit coupling-enhanced valley polarisation and the large density of states below half filling of the moiré band in twisted bilayer graphene coupled to tungsten diselenide. We observe an anomalous Hall effect, accompanied by a series of Lifshitz transitions that are highly tunable with carrier density and magnetic field. The magnetisation shows an abrupt change of sign near half-filling, confirming its orbital nature. While the Hall resistance is not quantised at zero magnetic fields-indicating a ground state with partial valley polarisation-perfect quantisation and complete valley polarisation are observed at finite fields. Our results illustrate that singularities in the flat bands in the presence of spin-orbit coupling can stabilise ordered phases even at non-integer moiré band fillings.
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Affiliation(s)
- Saisab Bhowmik
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, 560012, India.
| | - Bhaskar Ghawri
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Youngju Park
- Department of Physics, University of Seoul, Seoul, 02504, Korea
| | - Dongkyu Lee
- Department of Physics, University of Seoul, Seoul, 02504, Korea
- Department of Smart Cities, University of Seoul, Seoul, 02504, Korea
| | - Suvronil Datta
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Radhika Soni
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, 560012, India
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki, 305-0044, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki, 305-0044, Japan
| | - Arindam Ghosh
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
- Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore, 560012, India
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, 02504, Korea.
- Department of Smart Cities, University of Seoul, Seoul, 02504, Korea.
| | - U Chandni
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, 560012, India.
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41
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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42
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Zhang C, Zhu T, Soejima T, Kahn S, Watanabe K, Taniguchi T, Zettl A, Wang F, Zaletel MP, Crommie MF. Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator. Nat Commun 2023; 14:3595. [PMID: 37328471 DOI: 10.1038/s41467-023-39110-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 05/25/2023] [Indexed: 06/18/2023] Open
Abstract
In recent years, correlated insulating states, unconventional superconductivity, and topologically non-trivial phases have all been observed in several moiré heterostructures. However, understanding of the physical mechanisms behind these phenomena is hampered by the lack of local electronic structure data. Here, we use scanning tunnelling microscopy and spectroscopy to demonstrate how the interplay between correlation, topology, and local atomic structure determines the behaviour of electron-doped twisted monolayer-bilayer graphene. Through gate- and magnetic field-dependent measurements, we observe local spectroscopic signatures indicating a quantum anomalous Hall insulating state with a total Chern number of ±2 at a doping level of three electrons per moiré unit cell. We show that the sign of the Chern number and associated magnetism can be electrostatically switched only over a limited range of twist angle and sample hetero-strain values. This results from a competition between the orbital magnetization of filled bulk bands and chiral edge states, which is sensitive to strain-induced distortions in the moiré superlattice.
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Grants
- Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center DOE | SC | Basic Energy Sciences (BES)
- KCWF16 DOE | SC | Basic Energy Sciences (BES)
- Molecular Foundry at LBNL DOE | SC | Basic Energy Sciences (BES)
- KCWF16 DOE | SC | Basic Energy Sciences (BES)
- Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center DOE | SC | Basic Energy Sciences (BES)
- KC2301 DOE | SC | Basic Energy Sciences (BES)
- KCWF16 DOE | SC | Basic Energy Sciences (BES)
- Molecular Foundry at LBNL DOE | SC | Basic Energy Sciences (BES)
- Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center DOE | SC | Basic Energy Sciences (BES)
- KCWF16 DOE | SC | Basic Energy Sciences (BES)
- Molecular Foundry at LBNL DOE | SC | Basic Energy Sciences (BES)
- Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center DOE | SC | Basic Energy Sciences (BES)
- KCWF16 DOE | SC | Basic Energy Sciences (BES)
- Molecular Foundry at LBNL DOE | SC | Basic Energy Sciences (BES)
- KC2301 DOE | SC | Basic Energy Sciences (BES)
- DMR-2221750 National Science Foundation (NSF)
- DMR-2221750 National Science Foundation (NSF)
- DMR-2221750 National Science Foundation (NSF)
- DMR-2221750 National Science Foundation (NSF)
- 20H00354, 21H05233, 23H02052 MEXT | Japan Society for the Promotion of Science (JSPS)
- 20H00354, 21H05233, 23H02052 MEXT | Japan Society for the Promotion of Science (JSPS)
- World Premier International Research Center Initiative (WPI) Ministry of Education, Culture, Sports, Science and Technology (MEXT)
- World Premier International Research Center Initiative (WPI) Ministry of Education, Culture, Sports, Science and Technology (MEXT)
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Affiliation(s)
- Canxun Zhang
- Department of Physics, University of California, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
- Kavli Energy NanoScience Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Tiancong Zhu
- Department of Physics, University of California, Berkeley, CA, 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
| | - Tomohiro Soejima
- Department of Physics, University of California, Berkeley, CA, 94720, USA
| | - Salman Kahn
- Department of Physics, University of California, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Alex Zettl
- Department of Physics, University of California, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
- Kavli Energy NanoScience Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Feng Wang
- Department of Physics, University of California, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
- Kavli Energy NanoScience Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA, 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
| | - Michael F Crommie
- Department of Physics, University of California, Berkeley, CA, 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
- Kavli Energy NanoScience Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
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43
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Wan X, Sarkar S, Lin SZ, Sun K. Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain. PHYSICAL REVIEW LETTERS 2023; 130:216401. [PMID: 37295089 DOI: 10.1103/physrevlett.130.216401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 04/26/2023] [Indexed: 06/12/2023]
Abstract
We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.
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Affiliation(s)
- Xiaohan Wan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Siddhartha Sarkar
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Shi-Zeng Lin
- Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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44
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Ghorashi SAA, Dunbrack A, Abouelkomsan A, Sun J, Du X, Cano J. Topological and Stacked Flat Bands in Bilayer Graphene with a Superlattice Potential. PHYSICAL REVIEW LETTERS 2023; 130:196201. [PMID: 37243639 DOI: 10.1103/physrevlett.130.196201] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 02/06/2023] [Accepted: 04/12/2023] [Indexed: 05/29/2023]
Abstract
We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with nonzero Chern numbers, C, including bands with higher Chern numbers |C|>1 and (ii) an unprecedented phase consisting of a stack of nearly perfect flat bands with C=0. For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. We further show that in the topological regime, the topological flat band has a favorable band geometry for realizing a fractional Chern insulator (FCI) and use exact diagonalization to show that the FCI is in fact the ground state at 1/3 filling. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena.
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Affiliation(s)
| | - Aaron Dunbrack
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Ahmed Abouelkomsan
- Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
| | - Jiacheng Sun
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Xu Du
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Jennifer Cano
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
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45
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Xu L, Li Y, Fang Y, Zheng H, Shi W, Chen C, Pei D, Lu D, Hashimoto M, Wang M, Yang L, Feng X, Zhang H, Huang F, Xue Q, He K, Liu Z, Chen Y. Topology Hierarchy of Transition Metal Dichalcogenides Built from Quantum Spin Hall Layers. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2300227. [PMID: 36870326 DOI: 10.1002/adma.202300227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2023] [Revised: 02/22/2023] [Indexed: 05/26/2023]
Abstract
The evolution of the physical properties of 2D material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase transition metal dichalcogenides (1T'-TMDs) with ubiquitous quantum spin Hall (QSH) states are ideal 2D building blocks of various 3D topological phases. However, the stacking geometry has been previously limited to the bulk 1T'-WTe2 type. Here, the novel 2M-TMDs consisting of translationally stacked 1T'-monolayers are introduced as promising material platforms with tunable inverted bandgaps and interlayer coupling. By performing advanced polarization-dependent angle-resolved photoemission spectroscopy as well as first-principles calculations on the electronic structure of 2M-TMDs, a topology hierarchy is revealed: 2M-WSe2 , MoS2, and MoSe2 are weak topological insulators (WTIs), whereas 2M-WS2 is a strong topological insulator (STI). Further demonstration of topological phase transitions by tunning interlayer distance indicates that band inversion amplitude and interlayer coupling jointly determine different topological states in 2M-TMDs. It is proposed that 2M-TMDs are parent compounds of various exotic phases including topological superconductors and promise great application potentials in quantum electronics due to their flexibility in patterning with 2D materials.
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Affiliation(s)
- Lixuan Xu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Yiwei Li
- Institute for Advanced Studies (IAS), Wuhan University, Wuhan, 430072, P. R. China
| | - Yuqiang Fang
- State Key Laboratory of Rare Earth Materials Chemistry and Applications College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, P. R. China
| | - Huijun Zheng
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- ShanghaiTech Laboratory for Topological Physics, Shanghai, 201210, P. R. China
| | - Wujun Shi
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- Center for Transformative Science, ShanghaiTech University, Shanghai, 201210, P. R. China
- Shanghai high repetition rate XFEL and extreme light facility (SHINE), ShanghaiTech University, Shanghai, 201210, P. R. China
| | - Cheng Chen
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Ding Pei
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- ShanghaiTech Laboratory for Topological Physics, Shanghai, 201210, P. R. China
| | - Donghui Lu
- Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Makoto Hashimoto
- Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Meixiao Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- ShanghaiTech Laboratory for Topological Physics, Shanghai, 201210, P. R. China
| | - Lexian Yang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Xiao Feng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Haijun Zhang
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing, 210093, P. R. China
| | - Fuqiang Huang
- State Key Laboratory of Rare Earth Materials Chemistry and Applications College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, P. R. China
| | - Qikun Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Ke He
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Zhongkai Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- ShanghaiTech Laboratory for Topological Physics, Shanghai, 201210, P. R. China
| | - Yulin Chen
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, P. R. China
- ShanghaiTech Laboratory for Topological Physics, Shanghai, 201210, P. R. China
- Clarendon LaboratoryDepartment of Physics, University of Oxford, Oxford, OX1 3PU, UK
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46
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Díez-Mérida J, Díez-Carlón A, Yang SY, Xie YM, Gao XJ, Senior J, Watanabe K, Taniguchi T, Lu X, Higginbotham AP, Law KT, Efetov DK. Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene. Nat Commun 2023; 14:2396. [PMID: 37100775 PMCID: PMC10133447 DOI: 10.1038/s41467-023-38005-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 04/06/2023] [Indexed: 04/28/2023] Open
Abstract
The coexistence of gate-tunable superconducting, magnetic and topological orders in magic-angle twisted bilayer graphene provides opportunities for the creation of hybrid Josephson junctions. Here we report the fabrication of gate-defined symmetry-broken Josephson junctions in magic-angle twisted bilayer graphene, where the weak link is gate-tuned close to the correlated insulator state with a moiré filling factor of υ = -2. We observe a phase-shifted and asymmetric Fraunhofer pattern with a pronounced magnetic hysteresis. Our theoretical calculations of the junction weak link-with valley polarization and orbital magnetization-explain most of these unconventional features. The effects persist up to the critical temperature of 3.5 K, with magnetic hysteresis observed below 800 mK. We show how the combination of magnetization and its current-induced magnetization switching allows us to realise a programmable zero-field superconducting diode. Our results represent a major advance towards the creation of future superconducting quantum electronic devices.
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Affiliation(s)
- J Díez-Mérida
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, 08860, Spain
| | - A Díez-Carlón
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, 08860, Spain
| | - S Y Yang
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, 08860, Spain
| | - Y-M Xie
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - X-J Gao
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - J Senior
- IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria
| | - K Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - X Lu
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, 08860, Spain
| | | | - K T Law
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Dmitri K Efetov
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, 08860, Spain.
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47
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Yu D, Li G, Wang L, Leykam D, Yuan L, Chen X. Moiré Lattice in One-Dimensional Synthetic Frequency Dimension. PHYSICAL REVIEW LETTERS 2023; 130:143801. [PMID: 37084429 DOI: 10.1103/physrevlett.130.143801] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 03/13/2023] [Indexed: 05/03/2023]
Abstract
The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of "moiré" lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.
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Affiliation(s)
- Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Guangzhen Li
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Luojia Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, 250358, China
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48
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Shen C, Ledwith PJ, Watanabe K, Taniguchi T, Khalaf E, Vishwanath A, Efetov DK. Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene. NATURE MATERIALS 2023; 22:316-321. [PMID: 36550373 DOI: 10.1038/s41563-022-01428-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands, and exhibits correlated quantum phases with electrical tunability. In this work, we demonstrate a spectroscopy technique that allows for dissociation of intertwined bands and quantification of the energy gaps and Chern numbers C of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and energy gaps in the flat bands. We uncover hard correlated gaps with C = 0 at integer moiré unit cell fillings of ν = 2 and 3 and reveal charge density wave states originating from van Hove singularities at fractional fillings ν = 5/3 and 11/3. In addition, we demonstrate displacement-field-driven first-order phase transitions at charge neutrality and ν = 2, which are consistent with a theoretical strong-coupling analysis, implying C2T symmetry breaking. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG and provide an avenue for investigating other related systems hosting both steep and flat bands.
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Affiliation(s)
- Cheng Shen
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, Spain.
| | | | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | | | - Eslam Khalaf
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Dmitri K Efetov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, Spain.
- Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), München, Germany.
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49
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Aggarwal D, Narula R, Ghosh S. A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:143001. [PMID: 36745922 DOI: 10.1088/1361-648x/acb984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 02/06/2023] [Indexed: 06/18/2023]
Abstract
The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp2carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.
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Affiliation(s)
| | - Rohit Narula
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
| | - Sankalpa Ghosh
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
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Cochran TA, Belopolski I, Manna K, Yahyavi M, Liu Y, Sanchez DS, Cheng ZJ, Yang XP, Multer D, Yin JX, Borrmann H, Chikina A, Krieger JA, Sánchez-Barriga J, Le Fèvre P, Bertran F, Strocov VN, Denlinger JD, Chang TR, Jia S, Felser C, Lin H, Chang G, Hasan MZ. Visualizing Higher-Fold Topology in Chiral Crystals. PHYSICAL REVIEW LETTERS 2023; 130:066402. [PMID: 36827563 DOI: 10.1103/physrevlett.130.066402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 01/18/2022] [Accepted: 12/14/2022] [Indexed: 06/18/2023]
Abstract
Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.
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Affiliation(s)
- Tyler A Cochran
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Ilya Belopolski
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Kaustuv Manna
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
- Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
| | - Mohammad Yahyavi
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Yiyuan Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Daniel S Sanchez
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Zi-Jia Cheng
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Xian P Yang
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Daniel Multer
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jia-Xin Yin
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Horst Borrmann
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Alla Chikina
- Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland
| | - Jonas A Krieger
- Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, 5232 Villigen, Switzerland
| | - Jaime Sánchez-Barriga
- Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein Strasse 15, 12489 Berlin, Germany
- IMDEA Nanoscience, C/ Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain
| | - Patrick Le Fèvre
- SOLEIL Synchrotron, L'Orme des Merisiers, Départementale 128, F-91190 Saint-Aubin, France
| | - François Bertran
- SOLEIL Synchrotron, L'Orme des Merisiers, Départementale 128, F-91190 Saint-Aubin, France
| | | | - Jonathan D Denlinger
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Tay-Rong Chang
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
| | - Shuang Jia
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Claudia Felser
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Hsin Lin
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Guoqing Chang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - M Zahid Hasan
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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