1
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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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Zhang H, Wei Y, Li Y, Lin S, Wang J, Taniguchi T, Watanabe K, Li J, Shi Y, Wang X, Shi Y, Fei Z. Layer-Dependent Electromechanical Response in Twisted Graphene Moiré Superlattices. ACS NANO 2024; 18:17570-17577. [PMID: 38934625 DOI: 10.1021/acsnano.4c01794] [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
The coupling of mechanical deformation and electrical stimuli at the nanoscale has been the subject of intense investigation in the realm of materials science. Recently, twisted van der Waals (vdW) materials have emerged as a platform for exploring exotic quantum states. These states are intimately tied to the formation of moiré superlattices, which can be visualized by directly exploiting the electromechanical response. However, the origin of the response, even in twisted bilayer graphene (tBLG), remains unsettled. Here, employing lateral piezoresponse force microscopy (LPFM), we investigate the electromechanical responses of marginally twisted graphene moiré superlattices with different layer thicknesses. We observe distinct LPFM amplitudes and spatial profiles in tBLG and twisted monolayer-bilayer graphene (tMBG), exhibiting effective in-plane piezoelectric coefficients of 0.05 and 0.35 pm/V, respectively. Force tuning experiments further underscored a marked divergence in their responses. The contrasting behaviors suggest different electromechanical couplings in tBLG and tMBG. In tBLG, the response near the domain walls is attributed to the flexoelectric effect, while in tMBG, the behaviors can be comprehended within the context of the piezoelectric effect. Our results not only provide insights into electromechanical and corporative effects in twisted vdW materials with different stacking symmetries but may also offer a way to engineer them at the nanoscale.
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Affiliation(s)
- Hanhao Zhang
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
| | - Yuanhao Wei
- State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China
| | - Yuhao Li
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou 215163, Jiangsu,China
| | - Shengsheng Lin
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
| | - Jiarui Wang
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jiangyu Li
- Guangdong Provisional Key Laboratory of Functional Oxide Materials and Devices, Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Yi Shi
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
| | - Xinran Wang
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
- School of Integrated Circuits, Nanjing University, Suzhou 215163, Jiangsu, China
- Suzhou Laboratory, Suzhou 215123, Jiangsu, China
| | - Yan Shi
- State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China
| | - Zaiyao Fei
- National Laboratory of Solid-State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Jiangsu, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou 215163, Jiangsu,China
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3
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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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4
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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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5
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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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6
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Zhumagulov Y, Kochan D, Fabian J. Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling. PHYSICAL REVIEW LETTERS 2024; 132:186401. [PMID: 38759183 DOI: 10.1103/physrevlett.132.186401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 11/28/2023] [Accepted: 03/22/2024] [Indexed: 05/19/2024]
Abstract
The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.
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Affiliation(s)
- Yaroslav Zhumagulov
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Denis Kochan
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
- Institute of Physics, Slovak Academy of Sciences, 84511 Bratislava, Slovakia
- Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan 70101, Taiwan
| | - Jaroslav Fabian
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
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7
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Li H, Xiang Z, Naik MH, Kim W, Li Z, Sailus R, Banerjee R, Taniguchi T, Watanabe K, Tongay S, Zettl A, da Jornada FH, Louie SG, Crommie MF, Wang F. Imaging moiré excited states with photocurrent tunnelling microscopy. NATURE MATERIALS 2024; 23:633-638. [PMID: 38172545 DOI: 10.1038/s41563-023-01753-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 11/06/2023] [Indexed: 01/05/2024]
Abstract
Moiré superlattices provide a highly tuneable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators to moiré excitons. Scanning tunnelling microscopy has played a key role in probing microscopic behaviours of the moiré correlated ground states at the atomic scale. However, imaging of quantum excited states in moiré heterostructures remains an outstanding challenge. Here we develop a photocurrent tunnelling microscopy technique that combines laser excitation and scanning tunnelling spectroscopy to directly visualize the electron and hole distribution within the photoexcited moiré exciton in twisted bilayer WS2. The tunnelling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the in-plane charge transfer moiré exciton in twisted bilayer WS2, predicted by our GW-Bethe-Salpeter equation calculations, that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our technique enables the exploration of photoexcited non-equilibrium moiré phenomena at the atomic scale.
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Affiliation(s)
- Hongyuan Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Graduate Group in Applied Science and Technology, University of California Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Ziyu Xiang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Graduate Group in Applied Science and Technology, University of California Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Mit H Naik
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Woochang Kim
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Zhenglu Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Renee Sailus
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Rounak Banerjee
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - 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
| | - Sefaattin Tongay
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Alex Zettl
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Felipe H da Jornada
- Department of Materials Science and Engineering, Stanford University, Palo Alto, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Steven G Louie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Michael F Crommie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Feng Wang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
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8
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Louis E, Chiappe G, Vergés JA, San-Fabián E. Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:778. [PMID: 38727373 PMCID: PMC11085075 DOI: 10.3390/nano14090778] [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: 02/28/2024] [Revised: 04/26/2024] [Accepted: 04/27/2024] [Indexed: 05/13/2024]
Abstract
The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.
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Affiliation(s)
- Enrique Louis
- Departamento de Física Aplicada, Instituto Universitario de Materiales de Alicante (IUMA), Universidad de Alicante, 03080 Alicante, Spain;
| | - Guillermo Chiappe
- Departamento de Física Aplicada, Instituto Universitario de Materiales de Alicante (IUMA), Universidad de Alicante, 03080 Alicante, Spain;
| | - José A. Vergés
- Departamento de Teoría y Simulación de Materiales, Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid, Spain;
| | - Emilio San-Fabián
- Departamento de Química Física, Instituto Universitario de Materiales de Alicante (IUMA), Universidad de Alicante, 03080 Alicante, Spain
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9
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Ke Y, Wan L, Qin X, Hu W, Yang J. Proposed Quantum Twisting Scanning Probe Microscope over Twisted Bilayer Graphene. NANO LETTERS 2024; 24:4433-4438. [PMID: 38564276 DOI: 10.1021/acs.nanolett.4c00205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
Twisted bilayer graphene (TBG) has the natural merits of tunable flat bands and localized states distributed as a triangular lattice. However, the application of this state remains obscure. By density functional theory (DFT) and pz orbital tight-binding model calculations, we investigate the tip-shaped electrostatic potential of top valence electrons of TBG at half filling. Adsorption energy scanning of molecules above the TBG reveals that this tip efficiently attracts molecules selectively to AA-stacked or AB-stacked regions. Tip shapes can be controlled by their underlying electronic structure, with electrons of low bandwidth exhibiting a more localized feature. Our results indicate that TBG tips offer applications in noninvasive and nonpolluting measurements in scanning probe microscopy and theoretical guidance for 2D material-based probes.
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Affiliation(s)
- Yifan Ke
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lingyun Wan
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xinming Qin
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wei Hu
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
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10
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Li K, Yin LJ, Che C, Zhang S, Liu X, Xiao Y, Liu S, Tong Q, Li SY, Pan A. Correlation-Induced Symmetry-Broken States in Large-Angle Twisted Bilayer Graphene on MoS 2. ACS NANO 2024; 18:7937-7944. [PMID: 38441035 DOI: 10.1021/acsnano.3c09993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
Strongly correlated states commonly emerge in twisted bilayer graphene (TBG) with "magic-angle" (1.1°), where the electron-electron (e-e) interaction U becomes prominent relative to the small bandwidth W of the nearly flat band. However, the stringent requirement of this magic angle makes the sample preparation and the further application facing great challenges. Here, using scanning tunneling microscopy (STM) and spectroscopy (STS), we demonstrate that the correlation-induced symmetry-broken states can also be achieved in a 3.45° TBG, via engineering this nonmagic-angle TBG into regimes of U/W > 1. We enhance the e-e interaction through controlling the microscopic dielectric environment by using a MoS2 substrate. Simultaneously, the width of the low-energy van Hove singularity (VHS) peak is reduced by enhancing the interlayer coupling via STM tip modulation. When partially filled, the VHS peak exhibits a giant splitting into two states flanked by the Fermi level and shows a symmetry-broken LDOS distribution with a stripy charge order, which confirms the existence of strong correlation effect in our 3.45° TBG. Our result demonstrates the feasibility of the study and application of the correlation physics in TBGs with a wider range of twist angle.
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Affiliation(s)
- Kaihui Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Long-Jing Yin
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Chenglong Che
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Shihao Zhang
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Xueying Liu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Yulong Xiao
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Songlong Liu
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Qingjun Tong
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Si-Yu Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
- Greater Bay Area Institute for Innovation, Hunan University, Guangzhou 511300, People's Republic of China
| | - Anlian Pan
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
- School of Physics and Electronics, Hunan Normal University, Changsha 410081, People's Republic of China
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11
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Cheng Y, Tang WQ, Geng LT, Xu M, Zhu JP, Meng SS, Gu ZY. Polar alcohol guest molecules regulate the stacking modes of 2-D MOF nanosheets. Chem Sci 2024; 15:4106-4113. [PMID: 38487231 PMCID: PMC10935662 DOI: 10.1039/d3sc06844g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 02/07/2024] [Indexed: 03/17/2024] Open
Abstract
The modulation of two-dimensional metal-organic framework (2-D MOF) nanosheet stacking is an effective means to improve the properties and promote the application of nanosheets in various fields. Here, we employed a series of alcohol guest molecules (MeOH, EtOH and PrOH) to modulate Zr-BTB (BTB = benzene-1,3,5-tribenzoate) nanosheets and to generate untwisted stacking. The distribution of stacking angles was statistically analyzed from high-angle annular dark-field (HAADF) and fast Fourier transform (FFT) images. The ratios of untwisted stacking were calculated, such as 77.01% untwisted stacking for MeOH, 83.45% for EtOH, and 85.61% for PrOH. The obtained untwisted Zr-BTB showed good separation abilities for different substituted benzene isomers, superior para selectivity and excellent column stability and reusability. Control experiments of 2-D Zr-TCA (TCA = 4,4',4''-tricarboxytriphenylamine) and Zr-TATB (TATB = 4,4',4''-(1,3,5-triazine-2,4,6-triyl)tribenzoic acid) nanosheets with similar pore sizes and stronger polarity regulated by the alcohol guests exhibited moderate separation performance. The electron microscopy images revealed that polar alcohol regulation dominantly generated the twisted stacking of Zr-TCA and Zr-TATB with various Moiré patterns. Polar guest molecules, such as alcohols, provide strong host-guest interactions during the regulation of MOF nanosheet stacking, providing an opportunity to design new porous Moiré materials with application prospects.
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Affiliation(s)
- Yue Cheng
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Wen-Qi Tang
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Lu-Ting Geng
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Ming Xu
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Jian-Ping Zhu
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Sha-Sha Meng
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
| | - Zhi-Yuan Gu
- Jiangsu Key Laboratory of Biofunctional Materials, Jiangsu Collaborative Innovation Center of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University Nanjing 210023 China
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12
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Poduval PP, Scheurer MS. Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices. Nat Commun 2024; 15:1713. [PMID: 38402211 PMCID: PMC10894192 DOI: 10.1038/s41467-024-45950-4] [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: 07/19/2023] [Accepted: 02/08/2024] [Indexed: 02/26/2024] Open
Abstract
Stacking and twisting graphene layers allows to create and control a two-dimensional electron liquid with strong correlations. Experiments indicate that these systems exhibit strong tendencies towards both magnetism and triplet superconductivity. Motivated by this phenomenology, we study a 2D model of fluctuating triplet pairing and spin magnetism. Individually, their respective order parameters, d and N, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-4e superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite d ⋅ N, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi level can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This provides a possible explanation for recent tunneling experiments in the superconducting phase of graphene moiré systems.
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Affiliation(s)
- Prathyush P Poduval
- Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA, 92697, USA.
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
| | - Mathias S Scheurer
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany.
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, A-6020, Austria.
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13
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Liu K, Zheng J, Sha Y, Lyu B, Li F, Park Y, Ren Y, Watanabe K, Taniguchi T, Jia J, Luo W, Shi Z, Jung J, Chen G. Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene. NATURE NANOTECHNOLOGY 2024; 19:188-195. [PMID: 37996516 DOI: 10.1038/s41565-023-01558-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 10/30/2023] [Indexed: 11/25/2023]
Abstract
Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon-polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin-valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.
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Affiliation(s)
- Kai Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Jian Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Yating Sha
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Bosai Lyu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Fengping Li
- Department of Physics, University of Seoul, Seoul, Korea
| | - Youngju Park
- Department of Physics, University of Seoul, Seoul, Korea
| | - Yulu Ren
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Jinfeng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Weidong Luo
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Zhiwen Shi
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, Korea.
- Department of Smart Cities, University of Seoul, Seoul, Korea.
| | - Guorui Chen
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
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14
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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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15
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Kuang X, Pantaleón Peralta PA, Angel Silva-Guillén J, Yuan S, Guinea F, Zhan Z. Optical properties and plasmons in moiré structures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:173001. [PMID: 38232397 DOI: 10.1088/1361-648x/ad1f8c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 01/17/2024] [Indexed: 01/19/2024]
Abstract
The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.
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Affiliation(s)
- Xueheng Kuang
- Yangtze Delta Industrial Innovation Center of Quantum Science and Technology, Suzhou 215000, People's Republic of China
| | | | - Jose Angel Silva-Guillén
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
| | - Shengjun Yuan
- Key Laboratory of Artificial Micro- and Nano-structures of the Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, People's Republic of China
- Wuhan Institute of Quantum Technology, Wuhan 430206, People's Republic of China
| | - Francisco Guinea
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
- Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain
| | - Zhen Zhan
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
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16
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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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17
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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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18
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Montanaro A, Piccinini G, Mišeikis V, Sorianello V, Giambra MA, Soresi S, Giorgi L, D'Errico A, Watanabe K, Taniguchi T, Pezzini S, Coletti C, Romagnoli M. Sub-THz wireless transmission based on graphene-integrated optoelectronic mixer. Nat Commun 2023; 14:6471. [PMID: 37833246 PMCID: PMC10575943 DOI: 10.1038/s41467-023-42194-6] [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: 03/29/2023] [Accepted: 10/03/2023] [Indexed: 10/15/2023] Open
Abstract
Optoelectronics is a valuable solution to scale up wireless links frequency to sub-THz in the next generation antenna systems and networks. Here, we propose a low-power consumption, small footprint building block for 6 G and 5 G new radio wireless transmission allowing broadband capacity (e.g., 10-100 Gb/s per link and beyond). We demonstrate a wireless datalink based on graphene, reaching setup limited sub-THz carrier frequency and multi-Gbit/s data rate. Our device consists of a graphene-based integrated optoelectronic mixer capable of mixing an optically generated reference oscillator approaching 100 GHz, with a baseband electrical signal. We report >96 GHz optoelectronic bandwidth and -44 dB upconversion efficiency with a footprint significantly smaller than those of state-of-the-art photonic transmitters (i.e., <0.1 mm2). These results are enabled by an integrated-photonic technology based on wafer-scale high-mobility graphene and pave the way towards the development of optoelectronics-based arrayed-antennas for millimeter-wave technology.
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Affiliation(s)
- Alberto Montanaro
- Photonic Networks and Technologies Lab - CNIT, Via G. Moruzzi,1, 56124, Pisa, Italy.
- TeCIP Institute, Scuola Superiore Sant'Anna, via G. Moruzzi 1, 56124, Pisa, Italy.
| | - Giulia Piccinini
- NEST, Scuola Normale Superiore, Piazza San Silvestro 12, 56127, Pisa, Italy
- Center for Nanotechnology Innovation @NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127, Pisa, Italy
| | - Vaidotas Mišeikis
- Center for Nanotechnology Innovation @NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127, Pisa, Italy
- Graphene Labs, Istituto Italiano di Tecnologia, Via Morego 30, 16163, Genova, Italy
| | - Vito Sorianello
- Photonic Networks and Technologies Lab - CNIT, Via G. Moruzzi,1, 56124, Pisa, Italy
| | - Marco A Giambra
- Inphotec, CamGraPhIC srl, via G. Moruzzi 1, 56124, Pisa, Italy
| | - Stefano Soresi
- Inphotec, CamGraPhIC srl, via G. Moruzzi 1, 56124, Pisa, Italy
| | - Luca Giorgi
- Ericsson Research, via G. Moruzzi 1, 56124, Pisa, Italy
| | | | - K Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Sergio Pezzini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, P.zza S. Silvestro 12, 56127, Pisa, Italy
| | - Camilla Coletti
- Center for Nanotechnology Innovation @NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127, Pisa, Italy
- Graphene Labs, Istituto Italiano di Tecnologia, Via Morego 30, 16163, Genova, Italy
| | - Marco Romagnoli
- Photonic Networks and Technologies Lab - CNIT, Via G. Moruzzi,1, 56124, Pisa, Italy
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19
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Devakul T, Ledwith PJ, Xia LQ, Uri A, de la Barrera SC, Jarillo-Herrero P, Fu L. Magic-angle helical trilayer graphene. SCIENCE ADVANCES 2023; 9:eadi6063. [PMID: 37672575 PMCID: PMC10482339 DOI: 10.1126/sciadv.adi6063] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2023] [Accepted: 08/02/2023] [Indexed: 09/08/2023]
Abstract
We propose magic-angle helical trilayer graphene (HTG), a helical structure featuring identical rotation angles between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure realizing flat topological bands carrying nontrivial valley Chern number. These bands feature near-ideal quantum geometry and are isolated from remote bands by a very large energy gap, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states.
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Affiliation(s)
- Trithep Devakul
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Stanford University, Stanford, CA 94305, USA
| | | | - Li-Qiao Xia
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Aviram Uri
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Sergio C. de la Barrera
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada
| | - Pablo Jarillo-Herrero
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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20
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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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21
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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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22
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Uri A, de la Barrera SC, Randeria MT, Rodan-Legrain D, Devakul T, Crowley PJD, Paul N, Watanabe K, Taniguchi T, Lifshitz R, Fu L, Ashoori RC, Jarillo-Herrero P. Superconductivity and strong interactions in a tunable moiré quasicrystal. Nature 2023; 620:762-767. [PMID: 37468640 DOI: 10.1038/s41586-023-06294-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/07/2023] [Indexed: 07/21/2023]
Abstract
Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.
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Affiliation(s)
- Aviram Uri
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | | | - Mallika T Randeria
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Daniel Rodan-Legrain
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Trithep Devakul
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Philip J D Crowley
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Nisarga Paul
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - 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
| | - Ron Lifshitz
- Raymond & Beverly Sackler School of Physics & Astronomy, Tel Aviv University, Tel Aviv, Israel
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Raymond C Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
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23
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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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24
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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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25
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Chou YZ, Das Sarma S. Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:026501. [PMID: 37505969 DOI: 10.1103/physrevlett.131.026501] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 06/02/2023] [Indexed: 07/30/2023]
Abstract
We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.
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Affiliation(s)
- Yang-Zhi Chou
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Sankar Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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26
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Sainz-Cruz H, Pantaleón PA, Phong VT, Jimeno-Pozo A, Guinea F. Junctions and Superconducting Symmetry in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:016003. [PMID: 37478460 DOI: 10.1103/physrevlett.131.016003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 05/31/2023] [Indexed: 07/23/2023]
Abstract
Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. We analyze junctions between a scanning tunneling microscope (STM) tip and superconducting twisted bilayer graphene (TBG) and TBG Josephson junctions (JJs). We compare superconducting phases that are even or odd under valley exchange (s- or f-wave). The critical current in mixed (s and f) JJs strongly depends on the angle between the junction and the lattice. In STM-TBG junctions, due to Andreev reflection, the f-wave leads to a prominent peak in subgap conductance, as seen in experiments.
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Affiliation(s)
| | | | - Võ Tiến Phong
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | | | - Francisco Guinea
- Imdea Nanoscience, Faraday 9, 28015 Madrid, Spain
- Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastian, Spain
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27
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Hu Q, Zhan Z, Cui H, Zhang Y, Jin F, Zhao X, Zhang M, Wang Z, Zhang Q, Watanabe K, Taniguchi T, Cao X, Liu WM, Wu F, Yuan S, Xu Y. Observation of Rydberg moiré excitons. Science 2023; 380:1367-1372. [PMID: 37384701 DOI: 10.1126/science.adh1506] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/24/2023] [Indexed: 07/01/2023]
Abstract
Rydberg excitons, the solid-state counterparts of Rydberg atoms, have sparked considerable interest with regard to the harnessing of their quantum application potentials, but realizing their spatial confinement and manipulation poses a major challenge. Lately, the rise of two-dimensional moiré superlattices with highly tunable periodic potentials provides a possible pathway. Here, we experimentally demonstrate this capability through the spectroscopic evidence of Rydberg moiré excitons (XRM), which are moiré-trapped Rydberg excitons in monolayer semiconductor tungsten diselenide adjacent to twisted bilayer graphene. In the strong coupling regime, the XRM manifest as multiple energy splittings, pronounced red shift, and narrowed linewidth in the reflectance spectra, highlighting their charge-transfer character wherein electron-hole separation is enforced by strongly asymmetric interlayer Coulomb interactions. Our findings establish the excitonic Rydberg states as candidates for exploitation in quantum technologies.
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Affiliation(s)
- Qianying Hu
- 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
- School of Physics, Nankai University, Tianjin 300071, China
| | - Zhen Zhan
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Imdea Nanoscience, 28015 Madrid, Spain
| | - Huiying Cui
- 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
| | - Yalei Zhang
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Feng Jin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xuan 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
| | - Mingjie 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
| | - Zhichuan 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
| | - Qingming Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
| | - Kenji Watanabe
- Research Center for Functional 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
| | - Xuewei Cao
- School of Physics, Nankai University, Tianjin 300071, China
| | - Wu-Ming 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
| | - Fengcheng Wu
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
| | - Shengjun Yuan
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, 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
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28
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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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29
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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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30
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Dong Z, Ogunnaike O, Levitov L. Collective Excitations in Chiral Stoner Magnets. PHYSICAL REVIEW LETTERS 2023; 130:206701. [PMID: 37267555 DOI: 10.1103/physrevlett.130.206701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Revised: 02/21/2023] [Accepted: 04/07/2023] [Indexed: 06/04/2023]
Abstract
We argue that spin- and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The chiral edge behavior originates from the interplay between the momentum-space Berry curvature in Dirac bands and the geometric phase of a spin texture in position space. The edge modes are weakly confined to the edge, featuring dispersion that is robust and insensitive to the detailed profile of magnetization at the edge. This unique character of edge modes reduces their overlap with edge disorder and enhances the mode lifetime. The mode propagation direction reverses upon reversing valley polarization, an effect that provides a clear testable signature of geometric interactions in isospin-polarized Dirac bands.
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Affiliation(s)
- Zhiyu Dong
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Olumakinde Ogunnaike
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Leonid Levitov
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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31
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Pham PV, Mai TH, Do HB, Ponnusamy VK, Chuang FC. Integrated Graphene Heterostructures in Optical Sensing. MICROMACHINES 2023; 14:mi14051060. [PMID: 37241683 DOI: 10.3390/mi14051060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2023] [Revised: 05/14/2023] [Accepted: 05/14/2023] [Indexed: 05/28/2023]
Abstract
Graphene-an outstanding low-dimensional material-exhibited many physics behaviors that are unknown over the past two decades, e.g., exceptional matter-light interaction, large light absorption band, and high charge carrier mobility, which can be adjusted on arbitrary surfaces. The deposition approaches of graphene on silicon to form the heterostructure Schottky junctions was studied, unveiling new roadmaps to detect the light at wider-ranged absorption spectrums, e.g., far-infrared via excited photoemission. In addition, heterojunction-assisted optical sensing systems enable the active carriers' lifetime and, thereby, accelerate the separation speed and transport, and then they pave new strategies to tune high-performance optoelectronics. In this mini-review, an overview is considered concerning recent advancements in graphene heterostructure devices and their optical sensing ability in multiple applications (ultrafast optical sensing system, plasmonic system, optical waveguide system, optical spectrometer, or optical synaptic system) is discussed, in which the prominent studies for the improvement of performance and stability, based on the integrated graphene heterostructures, have been reported and are also addressed again. Moreover, the pros and cons of graphene heterostructures are revealed along with the syntheses and nanofabrication sequences in optoelectronics. Thereby, this gives a variety of promising solutions beyond the ones presently used. Eventually, the development roadmap of futuristic modern optoelectronic systems is predicted.
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Affiliation(s)
- Phuong V Pham
- Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
| | - The-Hung Mai
- Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
| | - Huy-Binh Do
- Faculty of Applied Science, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 700000, Vietnam
| | - Vinoth Kumar Ponnusamy
- Department of Medicinal and Applied Chemistry and Research Center for Precision Environmental Medicine, Kaohsiung Medical University (KMU), Kaohsiung 807, Taiwan
- Department of Medical Research, Kaohsiung Medical University Hospital (KMUH), Kaohsiung 807, Taiwan
- Department of Chemistry, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
| | - Feng-Chuan Chuang
- Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
- Center for Theoretical and Computational Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
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32
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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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33
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Qin W, Huang C, Wolf T, Wei N, Blinov I, MacDonald AH. Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 130:146001. [PMID: 37084431 DOI: 10.1103/physrevlett.130.146001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Revised: 10/01/2022] [Accepted: 03/16/2023] [Indexed: 05/03/2023]
Abstract
We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. The degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is d-wave-like and spin singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.
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Affiliation(s)
- Wei Qin
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Chunli Huang
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
- Theoretical Division, T-4, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Tobias Wolf
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Nemin Wei
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Igor Blinov
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Allan H MacDonald
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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34
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Gu S, Liu W, Mi S, Xian G, Guo J, Pang F, Chen S, Yang H, Gao HJ, Cheng Z. Twist angle-dependent work functions in CVD-grown twisted bilayer graphene probed by Kelvin probe force microscopy. NANOSCALE 2023; 15:5825-5833. [PMID: 36857709 DOI: 10.1039/d2nr07242d] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Tailoring the interlayer twist angle of bilayer graphene (BLG) significantly affects its electronic properties, including its superconductivity, topological transitions, ferromagnetic states, and correlated insulating states. These exotic electronic properties are sensitive to the work functions of BLG samples. In this study, the twist angle-dependent work functions of chemical vapour deposition-grown twisted bilayer graphene (tBLG) were investigated in detail using Kelvin probe force microscopy (KPFM) in combination with Raman spectroscopy. The thickness-dependent surface potentials of Bernal-stacked multilayer graphene were measured. It is found that with the increase in the number of layers, the work function decreases and tends to saturate. Bernal-stacked BLG and tBLG were determined via KPFM due to their twist angle-specific surface potentials. The detailed relationship between the twist angle and surface potential was determined via in situ KPFM and Raman spectral measurements. With the increase in the twist angle, the work function of tBLG will increase rapidly and then increase slowly when it is greater than 5°. The thermal stability of tBLG was investigated through a controlled annealing process. tBLG will become Bernal-stacked BLG after annealing at 350 °C. Our work provides the twist angle-dependent surface potentials of tBLG and provides the relevant conditions for the stability of the twist angle, which lays the foundation for further exploration of its twist angle-dependent electronic properties.
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Affiliation(s)
- Shangzhi Gu
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
| | - Wenyu Liu
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
| | - Shuo Mi
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
| | - Guoyu Xian
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
| | - Jiangfeng Guo
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
| | - Fei Pang
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
| | - Shanshan Chen
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
| | - Haitao Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
| | - Hong-Jun Gao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
| | - Zhihai Cheng
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China.
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35
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Pang J, Peng S, Hou C, Zhao H, Fan Y, Ye C, Zhang N, Wang T, Cao Y, Zhou W, Sun D, Wang K, Rümmeli MH, Liu H, Cuniberti G. Applications of Graphene in Five Senses, Nervous System, and Artificial Muscles. ACS Sens 2023; 8:482-514. [PMID: 36656873 DOI: 10.1021/acssensors.2c02790] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Graphene remains of great interest in biomedical applications because of biocompatibility. Diseases relating to human senses interfere with life satisfaction and happiness. Therefore, the restoration by artificial organs or sensory devices may bring a bright future by the recovery of senses in patients. In this review, we update the most recent progress in graphene based sensors for mimicking human senses such as artificial retina for image sensors, artificial eardrums, gas sensors, chemical sensors, and tactile sensors. The brain-like processors are discussed based on conventional transistors as well as memristor related neuromorphic computing. The brain-machine interface is introduced for providing a single pathway. Besides, the artificial muscles based on graphene are summarized in the means of actuators in order to react to the physical world. Future opportunities remain for elevating the performances of human-like sensors and their clinical applications.
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Affiliation(s)
- Jinbo Pang
- Collaborative Innovation Center of Technology and Equipment for Biological Diagnosis and Therapy in Universities of Shandong, Institute for Advanced Interdisciplinary Research (iAIR), University of Jinan, Jinan 250022, China
| | - Songang Peng
- High-Frequency High-Voltage Device and Integrated Circuits R&D Center and Key Laboratory of Microelectronic Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
| | - Chongyang Hou
- Collaborative Innovation Center of Technology and Equipment for Biological Diagnosis and Therapy in Universities of Shandong, Institute for Advanced Interdisciplinary Research (iAIR), University of Jinan, Jinan 250022, China
| | - Hongbin Zhao
- State Key Laboratory of Advanced Materials for Smart Sensing, GRINM Group Co. Ltd., Xinwai Street 2, Beijing 100088, People's Republic of China
| | - Yingju Fan
- School of Chemistry and Chemical Engineering, University of Jinan, Shandong, Jinan 250022, China
| | - Chen Ye
- School of Chemistry and Chemical Engineering, University of Jinan, Shandong, Jinan 250022, China
| | - Nuo Zhang
- School of Chemistry and Chemical Engineering, University of Jinan, Shandong, Jinan 250022, China
| | - Ting Wang
- State Key Laboratory of Biobased Material and Green Papermaking and People's Republic of China School of Bioengineering, Qilu University of Technology, Shandong Academy of Sciences, No. 3501 Daxue Road, Jinan 250353, People's Republic of China
| | - Yu Cao
- Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology (Ministry of Education) and School of Electrical Engineering, Northeast Electric Power University, Jilin 132012, China
| | - Weijia Zhou
- Collaborative Innovation Center of Technology and Equipment for Biological Diagnosis and Therapy in Universities of Shandong, Institute for Advanced Interdisciplinary Research (iAIR), University of Jinan, Jinan 250022, China
| | - Ding Sun
- School of Electrical and Computer Engineering, Jilin Jianzhu University, Changchun 130118, P. R. China
| | - Kai Wang
- School of Electrical Engineering, Weihai Innovation Research Institute, Qingdao University, Qingdao 266000, China
| | - Mark H Rümmeli
- Leibniz Institute for Solid State and Materials Research Dresden, Dresden, D-01171, Germany.,College of Energy, Soochow Institute for Energy and Materials Innovations, and Key Laboratory of Advanced Carbon Materials and Wearable Energy Technologies of Jiangsu Province, Soochow University, Suzhou 215006, China.,Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie Sklodowskiej 34, Zabrze 41-819, Poland.,Institute for Complex Materials, IFW Dresden, 20 Helmholtz Strasse, Dresden 01069, Germany.,Center for Energy and Environmental Technologies, VŠB-Technical University of Ostrava, 17. Listopadu 15, Ostrava 708 33, Czech Republic
| | - Hong Liu
- Collaborative Innovation Center of Technology and Equipment for Biological Diagnosis and Therapy in Universities of Shandong, Institute for Advanced Interdisciplinary Research (iAIR), University of Jinan, Jinan 250022, China.,State Key Laboratory of Crystal Materials, Center of Bio & Micro/Nano Functional Materials, Shandong University, 27 Shandanan Road, Jinan 250100, China
| | - Gianaurelio Cuniberti
- Institute for Materials Science and Max Bergmann Center of Biomaterials and Center for Advancing Electronics Dresden, Technische Universität Dresden, Dresden 01069, Germany
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36
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Kolář K, Shavit G, Mora C, Oreg Y, von Oppen F. Anderson's Theorem for Correlated Insulating States in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 130:076204. [PMID: 36867804 DOI: 10.1103/physrevlett.130.076204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under PT, where P and T denote particle-hole conjugation and time reversal, respectively. In contrast, PT-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states.
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Affiliation(s)
- Kryštof Kolář
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Gal Shavit
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 7610001
| | - Christophe Mora
- Université Paris Cité, CNRS, Laboratoire Matériaux et Phénomènes Quantiques, 75013 Paris, France
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 7610001
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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37
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Vogl M, Chaudhary S, Fiete GA. Light driven magnetic transitions in transition metal dichalcogenide heterobilayers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:095801. [PMID: 36560921 DOI: 10.1088/1361-648x/acab49] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 12/13/2022] [Indexed: 06/17/2023]
Abstract
Motivated by the recent excitement around the physics of twisted transition metal dichalcogenide (TMD) multilayer systems, we study strongly correlated phases of TMD heterobilayers under the influence of light. We consider both waveguide light and circularly polarized light. The former allows for longitudinally polarized light, which in the high frequency limit can be used to selectively modify interlayer hoppings in a tight-binding model. We argue based on quasi-degenerate perturbation theory that changes to the interlayer hoppings can be captured as a modulation to the strength of the moiré potential in a continuum model. As a consequence, waveguide light can be used to drive transitions between a myriad of different magnetic phases, including a transition from a 120∘Neel phase to a stripe ordered magnetic phase, or from a spin density wave phase to a paramagnetic phase, among others. When the system is subjected to circularly polarized light we find that the effective mass of the active TMD layer is modified by an applied electromagnetic field. By simultaneously applying waveguide light and circularly polarized light to a system, one has a high level of control in moving through the phase diagram in-situ. Lastly, we comment on the experimental feasibility of Floquet state preparation and argue that it is within reach of available techniques when the system is coupled to a judiciously chosen bath.
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Affiliation(s)
- Michael Vogl
- Department of Physics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
| | - Swati Chaudhary
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, United States of America
- Department of Physics, Northeastern University, Boston, MA 02115, United States of America
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
| | - Gregory A Fiete
- Department of Physics, Northeastern University, Boston, MA 02115, United States of America
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
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38
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Li SY, Wang Z, Xue Y, Wang Y, Zhang S, Liu J, Zhu Z, Watanabe K, Taniguchi T, Gao HJ, Jiang Y, Mao J. Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene. Nat Commun 2022; 13:4225. [PMID: 35869069 PMCID: PMC9307793 DOI: 10.1038/s41467-022-31851-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 07/05/2022] [Indexed: 11/22/2022] Open
Abstract
Flat bands in Van der Waals heterostructure provide an ideal platform for unveiling emergent quantum electronic phases. One celebrated example is twisted monolayer-bilayer graphene, in which the effects of electronic correlation have been observed. Here, we report the observation via scanning tunnelling microscopy and spectroscopy of correlated insulating states in twisted monolayer-bilayer graphene, leading to the formation of an electron crystal phase. At integer fillings, the strong Coulomb interaction redistributes flat-band electrons within one moiré unit cell, producing an insulating state with vanishing density of states at the Fermi level. Moreover, our approach enables the direct visualization of an ordered lattice of topological torus-shaped states, generated by the interaction between the electron crystal and the non-trivial band topology of twisted monolayer-bilayer graphene. Our results illustrate an efficient strategy for entwining topological physics with strong electron correlation in twisted van der Waals structures. Twisted van der Waals structures represent a versatile platform to investigate topological and correlated electronic states. Here, the authors report the visualization of an electron crystal phase in twisted monolayer-bilayer graphene via scanning tunnelling microscopy, studying the coupling between strong electron correlation and nontrivial band topology.
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39
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Su X, Huang T, Zheng B, Wang J, Wang X, Yan S, Wang X, Shi Y. Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene. NANO LETTERS 2022; 22:8975-8982. [PMID: 36374517 DOI: 10.1021/acs.nanolett.2c03220] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Moiré superlattices provide in-plane quantum restriction for light-matter interactions in twisted bilayer graphene (tBLG), leading to the exotic photon-Moiré physics and potential applications for light manipulation. Recently, our experiment identified a highly confined slow surface plasmons polaritons (SPPs) mode in tBLG. Here, we demonstrate that the propagation of the slow SPPs mode in tBLG is spatially tailored and steered at deep subwavelengths. Analysis by the perturbation theory indicates that the coupling between the slow SPPs mode and the Moiré system is greatly strengthened, which regulates the wavefront at the atomic scale and makes tBLG serve as a universal optical metamaterial. Consequently, the negative refraction is achieved at the interface of monolayer graphene and tBLG, by which a metalens with a controllable focal length and an extremely high resolution up to 1/150 of wavelength is devised. Our work paves the way for constructing optical metamaterial at the atomic scale and develops future photon-Moiré interaction systems.
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Affiliation(s)
- Xin Su
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Tianye Huang
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Binjie Zheng
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Junzhuan Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Xinran Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Shancheng Yan
- School of Geography and Biological Information, Nanjing University of Posts and Telecommunications, Nanjing210023, China
| | - Xiaomu Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
| | - Yi Shi
- Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing210093, China
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40
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Huang C, Wei N, Qin W, MacDonald AH. Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2022; 129:187001. [PMID: 36374687 DOI: 10.1103/physrevlett.129.187001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 07/26/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i) applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii) changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid ^{3}He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. We comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.
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Affiliation(s)
- Chunli Huang
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Nemin Wei
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Wei Qin
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Allan H MacDonald
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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41
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Li H, Fabbris G, Said AH, Sun JP, Jiang YX, Yin JX, Pai YY, Yoon S, Lupini AR, Nelson CS, Yin QW, Gong CS, Tu ZJ, Lei HC, Cheng JG, Hasan MZ, Wang Z, Yan B, Thomale R, Lee HN, Miao H. Discovery of conjoined charge density waves in the kagome superconductor CsV 3Sb 5. Nat Commun 2022; 13:6348. [PMID: 36289236 PMCID: PMC9606281 DOI: 10.1038/s41467-022-33995-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 10/07/2022] [Indexed: 11/09/2022] Open
Abstract
The electronic instabilities in CsV3Sb5 are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV3Sb5, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L1-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV3Sb5 go beyond the minimal framework of kagome electronic bands near van Hove filling.
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Affiliation(s)
- Haoxiang Li
- grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA ,grid.24515.370000 0004 1937 1450Present Address: Advanced Materials Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong 511453 China
| | - G. Fabbris
- grid.187073.a0000 0001 1939 4845Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439 USA
| | - A. H. Said
- grid.187073.a0000 0001 1939 4845Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439 USA
| | - J. P. Sun
- grid.9227.e0000000119573309Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China ,grid.410726.60000 0004 1797 8419School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190 China
| | - Yu-Xiao Jiang
- grid.16750.350000 0001 2097 5006Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, NJ 08544 USA
| | - J.-X. Yin
- grid.263817.90000 0004 1773 1790Laboratory for Quantum Emergence, Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055 China
| | - Yun-Yi Pai
- grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA
| | - Sangmoon Yoon
- grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA ,grid.256155.00000 0004 0647 2973Present Address: Department of Physics, Gachon University, Seongnam, 13120 Republic of Korea
| | - Andrew R. Lupini
- grid.135519.a0000 0004 0446 2659Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA
| | - C. S. Nelson
- grid.202665.50000 0001 2188 4229National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973 USA
| | - Q. W. Yin
- grid.24539.390000 0004 0368 8103Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials and Microdevices, Renmin University of China, Beijing, 100872 China
| | - C. S. Gong
- grid.24539.390000 0004 0368 8103Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials and Microdevices, Renmin University of China, Beijing, 100872 China
| | - Z. J. Tu
- grid.24539.390000 0004 0368 8103Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials and Microdevices, Renmin University of China, Beijing, 100872 China
| | - H. C. Lei
- grid.24539.390000 0004 0368 8103Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials and Microdevices, Renmin University of China, Beijing, 100872 China
| | - J.-G. Cheng
- grid.9227.e0000000119573309Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China ,grid.410726.60000 0004 1797 8419School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190 China
| | - M. Z. Hasan
- grid.16750.350000 0001 2097 5006Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, NJ 08544 USA
| | - Ziqiang Wang
- grid.208226.c0000 0004 0444 7053Department of Physics, Boston College, Chestnut Hill, MA 02467 USA
| | - Binghai Yan
- grid.13992.300000 0004 0604 7563Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 7610001 Israel
| | - R. Thomale
- grid.8379.50000 0001 1958 8658Institute for Theoretical Physics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - H. N. Lee
- grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA
| | - H. Miao
- grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA
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42
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Baby skyrmions in Chern ferromagnets and topological mechanism for spin-polaron formation in twisted bilayer graphene. Nat Commun 2022; 13:6245. [PMID: 36271002 PMCID: PMC9587044 DOI: 10.1038/s41467-022-33673-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 09/21/2022] [Indexed: 11/17/2022] Open
Abstract
The advent of moiré materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials with electron-like charge carriers, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real-space description of skyrmions is ill-suited to address the limit of small skyrmions and to account for momentum-space band features. Here, we develop a momentum-space approach to study the formation of the smallest skyrmions – spin polarons, formed as bound states of an electron and a spin flip – in topological ferromagnets. We show that, quite generally, there is an attraction between an electron and a spin flip that is purely topological in origin, promoting the formation of spin polarons. Applying our results to twisted bilayer graphene, we identify a range of parameters where spin polarons are formed and discuss their possible experimental signatures. In conventional materials, charge carriers are electron-like quasiparticles, but topological bands allow for more exotic possibilities. Here, the authors predict that in the Chern-ferromagnet phase of twisted bilayer graphene charge is carried by spin polarons, bound states of an electron and a spin flip.
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43
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Goodwin ZAH, Fal'ko VI. Moiré modulation of charge density waves. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:494001. [PMID: 36223792 DOI: 10.1088/1361-648x/ac99ca] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 10/12/2022] [Indexed: 06/16/2023]
Abstract
Here we investigate how charge density waves (CDWs), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For3×3CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for2×2CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For3×3CDWs with twist angles close to 180∘, moiré-scale triangular structures can form; while close to 0∘, moiré-scale dimer domains occur. The star-of-David CDW (13×13) is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to the2×2CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré superlattice and CDW phases intrinsic to the comprising 2D materials.
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Affiliation(s)
- Zachary A H Goodwin
- National Graphene Institute, University of Manchester, Booth St. E., Manchester M13 9PL, United Kingdom
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Vladimir I Fal'ko
- National Graphene Institute, University of Manchester, Booth St. E., Manchester M13 9PL, United Kingdom
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Henry Royce Institute for Advanced Materials, University of Manchester, Manchester M13 9PL, United Kingdom
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44
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Zhang Y, Polski R, Lewandowski C, Thomson A, Peng Y, Choi Y, Kim H, Watanabe K, Taniguchi T, Alicea J, von Oppen F, Refael G, Nadj-Perge S. Promotion of superconductivity in magic-angle graphene multilayers. Science 2022; 377:1538-1543. [PMID: 36173835 DOI: 10.1126/science.abn8585] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Graphene moiré superlattices show an abundance of correlated insulating, topological, and superconducting phases. Whereas the origins of strong correlations and nontrivial topology can be directly linked to flat bands, the nature of superconductivity remains enigmatic. We demonstrate that magic-angle devices made of twisted tri-, quadri-, and pentalayer graphene placed on monolayer tungsten diselenide exhibit flavor polarization and superconductivity. We also observe insulating states in the tril- and quadrilayer arising at finite electric displacement fields. As the number of layers increases, superconductivity emerges over an enhanced filling-factor range, and in the pentalayer it extends well beyond the filling of four electrons per moiré unit cell. Our results highlight the role of the interplay between flat and more dispersive bands in extending superconducting regions in graphene moiré superlattices.
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Affiliation(s)
- Yiran Zhang
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Robert Polski
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Cyprian Lewandowski
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Alex Thomson
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, University of California, Davis, CA 95616, USA
| | - Yang Peng
- Department of Physics and Astronomy, California State University, Northridge, CA 91330, USA
| | - Youngjoon Choi
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Hyunjin Kim
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305 0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305 0044, Japan
| | - Jason Alicea
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Gil Refael
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Stevan Nadj-Perge
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
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45
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Hong JP, Soejima T, Zaletel MP. Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy. PHYSICAL REVIEW LETTERS 2022; 129:147001. [PMID: 36240422 DOI: 10.1103/physrevlett.129.147001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 08/20/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. By analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.
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Affiliation(s)
- Jung Pyo Hong
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
| | - Tomohiro Soejima
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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46
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Călugăru D, Regnault N, Oh M, Nuckolls KP, Wong D, Lee RL, Yazdani A, Vafek O, Bernevig BA. Spectroscopy of Twisted Bilayer Graphene Correlated Insulators. PHYSICAL REVIEW LETTERS 2022; 129:117602. [PMID: 36154402 DOI: 10.1103/physrevlett.129.117602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 07/13/2022] [Indexed: 06/16/2023]
Abstract
We analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at ±4 electrons/moiré unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral U(4) rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state.
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Affiliation(s)
- Dumitru Călugăru
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Nicolas Regnault
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Myungchul Oh
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Kevin P Nuckolls
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Dillon Wong
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Ryan L Lee
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Ali Yazdani
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Oskar Vafek
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
- Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Spain
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47
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Ramires A. Twisted-graphene model draws inspiration from heavy elements. Nature 2022; 608:474-475. [PMID: 35941385 DOI: 10.1038/d41586-022-02108-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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48
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Song Z, Wang Y, Zheng H, Narang P, Wang LW. Deep Quantum-Dot Arrays in Moiré Superlattices of Non-van der Waals Materials. J Am Chem Soc 2022; 144:14657-14667. [PMID: 35921553 DOI: 10.1021/jacs.2c04390] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Recently, moiré superlattices of twisted van der Waals (vdW) materials have attracted substantial interest due to their strongly correlated properties. However, the vdW interlayer interaction is intrinsically weak, such that many desired properties can only exist at low temperature. Here, we theoretically predict some unusual properties stemming from the chemical bonding between twisted PbS nanosheets as an example of non-vdW moiré superlattices. The strong interlayer coupling in such systems results in giant strain vortices and dipole vortices at the interface. The modified electronic structures become a series of dispersionless bands and artificial-atom states. In real space, these states are analogous to arrays of well-positioned quantum dots, which may be promising for use in single-electron devices. In theory, if the materials are doped with a low concentration of electrons, a Wigner crystal will form even without any magnetic field. To confirm the accessibility and stability of non-vdW moiré superlattices in experiment, we synthesized PbS moiré superlattices with different twist angles. Our transmission-electron-microscope observations reveal the resemblance of the small-angle-twisted structures with the square matrices of quantum dots, which is in good accordance with our calculations.
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Affiliation(s)
- Zhigang Song
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Yu Wang
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Haimei Zheng
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.,Department of Materials Science and Engineering, University of California, Berkeley, California 94720, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Lin-Wang Wang
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
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49
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Burg GW, Khalaf E, Wang Y, Watanabe K, Taniguchi T, Tutuc E. Emergence of correlations in alternating twist quadrilayer graphene. NATURE MATERIALS 2022; 21:884-889. [PMID: 35798944 DOI: 10.1038/s41563-022-01286-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 05/10/2022] [Indexed: 06/15/2023]
Abstract
Alternating twist multilayer graphene (ATMG) has recently emerged as a family of moiré systems that share several fundamental properties with twisted bilayer graphene, and are expected to host similarly strong electron-electron interactions near the magic angle. Here, we study alternating twist quadrilayer graphene (ATQG) samples with twist angles of 1.96° and 1.52°, which are slightly removed from the magic angle of 1.68°. At the larger angle, we find signatures of correlated insulators only when the ATQG is hole doped, and no signatures of superconductivity, and for the smaller angle we find evidence of superconductivity, while signs of the correlated insulators weaken. Our results provide insight into the twist angle dependence of correlated phases in ATMG and shed light on the nature of correlations in the intermediate coupling regime at the edge of the magic angle range where dispersion and interaction are of the same order.
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Affiliation(s)
- G William Burg
- Microelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA
| | - Eslam Khalaf
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics, The University of Texas at Austin, Austin, TX, USA
| | - Yimeng Wang
- Microelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute of Materials Science, Ibaraki, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute of Materials Science, Ibaraki, Japan
| | - Emanuel Tutuc
- Microelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA.
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50
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Park JM, Cao Y, Xia LQ, Sun S, Watanabe K, Taniguchi T, Jarillo-Herrero P. Robust superconductivity in magic-angle multilayer graphene family. NATURE MATERIALS 2022; 21:877-883. [PMID: 35798945 DOI: 10.1038/s41563-022-01287-1] [Citation(s) in RCA: 52] [Impact Index Per Article: 26.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2021] [Accepted: 05/10/2022] [Indexed: 06/15/2023]
Abstract
The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) established a new platform to explore interaction-driven and topological phenomena. However, despite multitudes of correlated phases observed in moiré systems, robust superconductivity appears the least common, found only in MATBG and more recently in magic-angle twisted trilayer graphene. Here we report the experimental realization of superconducting magic-angle twisted four-layer and five-layer graphene, hence establishing alternating twist magic-angle multilayer graphene as a robust family of moiré superconductors. This finding suggests that the flat bands shared by the members play a central role in the superconductivity. Our measurements in parallel magnetic fields, in particular the investigation of Pauli limit violation and spontaneous rotational symmetry breaking, reveal a clear distinction between the N = 2 and N > 2-layer structures, consistent with the difference between their orbital responses to magnetic fields. Our results expand the emergent family of moiré superconductors, providing new insight with potential implications for design of new superconducting materials platforms.
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Affiliation(s)
- Jeong Min Park
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Yuan Cao
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Li-Qiao Xia
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Shuwen Sun
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
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