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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 Y, Xie B, Yang Y, Wu Y, Lu X, Hu Y, Ding Y, He J, Dong P, Wang J, Zhou X, Liu J, Wang ZJ, Li J. Extremely large magnetoresistance in twisted intertwined graphene spirals. Nat Commun 2024; 15:6120. [PMID: 39033152 PMCID: PMC11271300 DOI: 10.1038/s41467-024-50456-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 07/10/2024] [Indexed: 07/23/2024] Open
Abstract
Extremely large magnetoresistance (XMR) is highly applicable in spintronic devices such as magnetic sensors, magnetic memory, and hard drives. Typically, XMR is found in Weyl semimetals characterized by perfect electron-hole symmetry or exceptionally high electric conductivity and mobility. Our study explores this phenomenon in a recently developed graphene moiré system, which demonstrates XMR owing to its topological structure and high-quality crystal formation. We investigate the electronic properties of three-dimensional intertwined twisted graphene spirals (TGS), manipulating the screw dislocation axis to achieve a rotation angle of 7.3°. Notably, at 14 T and 2 K, the magnetoresistance of these structures reaches 1.7 × 107%, accompanied by a metal-insulator transition as the temperature increases. This transition becomes noticeable when the magnetic field exceeds a minimal threshold of approximately 0.1 T. These observations suggest the possible existence of complex, correlated states within the partially filled three-dimensional Landau levels of the 3D TGS system. Our findings open up possibilities for achieving XMR by engineering the topological structure of 2D layered moiré systems.
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Affiliation(s)
- Yiwen Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Bo Xie
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Yue Yang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Yueshen Wu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Xin Lu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Yuxiong Hu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Yifan Ding
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Jiadian He
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Peng Dong
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Jinghui Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Xiang Zhou
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China.
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China.
- Liaoning Academy of Materials, Shenyang, China.
| | - Zhu-Jun Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China.
| | - Jun Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China.
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, China.
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3
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Chen M, Xie Y, Cheng B, Yang Z, Li XZ, Chen F, Li Q, Xie J, Watanabe K, Taniguchi T, He WY, Wu M, Liang SJ, Miao F. Selective and quasi-continuous switching of ferroelectric Chern insulator devices for neuromorphic computing. NATURE NANOTECHNOLOGY 2024; 19:962-969. [PMID: 38965346 DOI: 10.1038/s41565-024-01698-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 05/19/2024] [Indexed: 07/06/2024]
Abstract
Quantum materials exhibit dissipationless topological edge state transport with quantized Hall conductance, offering notable potential for fault-tolerant computing technologies. However, the development of topological edge state-based computing devices remains a challenge. Here we report the selective and quasi-continuous ferroelectric switching of topological Chern insulator devices, showcasing a proof-of-concept demonstration in noise-immune neuromorphic computing. We fabricate this ferroelectric Chern insulator device by encapsulating magic-angle twisted bilayer graphene with doubly aligned h-BN layers and observe the coexistence of the interfacial ferroelectricity and the topological Chern insulating states. The observed ferroelectricity exhibits an anisotropic dependence on the in-plane magnetic field. By tuning the amplitude of the gate voltage pulses, we achieve ferroelectric switching between any pair of Chern insulating states in the presence of a finite magnetic field, resulting in 1,280 ferroelectric states with distinguishable Hall resistance levels on a single device. Furthermore, we demonstrate deterministic switching between two arbitrary levels among the record-high number of ferroelectric states. This unique switching capability enables the implementation of a convolutional neural network resistant to external noise, utilizing the quantized Hall conductance levels of the Chern insulator device as weights. Our study provides a promising avenue towards the development of topological quantum neuromorphic computing, where functionality and performance can be drastically enhanced by topological quantum materials.
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Affiliation(s)
- Moyu Chen
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Yongqin Xie
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Bin Cheng
- Institute of Interdisciplinary Physical Sciences, School of Science, Nanjing University of Science and Technology, Nanjing, China.
| | - Zaizheng Yang
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Xin-Zhi Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Fanqiang Chen
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Qiao Li
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Jiao Xie
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Wen-Yu He
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Menghao Wu
- School of Physics and School of Chemistry, Institute of Theoretical Chemistry, Huazhong University of Science and Technology, Wuhan, China
| | - Shi-Jun Liang
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
| | - Feng Miao
- Institute of Brain-Inspired Intelligence, National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
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Singh K, Chew A, Herzog-Arbeitman J, Bernevig BA, Vafek O. Topological heavy fermions in magnetic field. Nat Commun 2024; 15:5257. [PMID: 38898060 PMCID: PMC11187166 DOI: 10.1038/s41467-024-49531-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 06/07/2024] [Indexed: 06/21/2024] Open
Abstract
The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method-based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.
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Affiliation(s)
- Keshav Singh
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
- Department of Physics, Florida State University, Tallahassee, FL, 32306, USA
| | - Aaron Chew
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | | | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018, Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Oskar Vafek
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA.
- Department of Physics, Florida State University, Tallahassee, FL, 32306, USA.
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Han X, Liu Q, Wang Y, Niu R, Qu Z, Wang Z, Li Z, Han C, Watanabe K, Taniguchi T, Song Z, Liu J, Mao J, Han Z, Chittari BL, Jung J, Gan Z, Lu J. Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice. NANO LETTERS 2024; 24:6286-6295. [PMID: 38747346 DOI: 10.1021/acs.nanolett.4c00948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.
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Affiliation(s)
- Xiangyan Han
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qianling Liu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yijie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Niu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuangzhuang Qu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhiyu Wang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuoxian Li
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Chunrui Han
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Zhida Song
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
| | - Jinhai Mao
- School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zheng Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Optoelectronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Bheema Lingam Chittari
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul 02504, Korea
- Department of Smart Cities, University of Seoul, Seoul 02504, Korea
| | - Zizhao Gan
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
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6
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Hoke JC, Li Y, May-Mann J, Watanabe K, Taniguchi T, Bradlyn B, Hughes TL, Feldman BE. Uncovering the spin ordering in magic-angle graphene via edge state equilibration. Nat Commun 2024; 15:4321. [PMID: 38773076 PMCID: PMC11109299 DOI: 10.1038/s41467-024-48385-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 04/30/2024] [Indexed: 05/23/2024] Open
Abstract
The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.
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Affiliation(s)
- Jesse C Hoke
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Yifan Li
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Julian May-Mann
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Barry Bradlyn
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Benjamin E Feldman
- Department of Physics, Stanford University, Stanford, CA, 94305, USA.
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA.
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA.
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7
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Zhu X, Sun J, Feng S, Guo H. Moiré band renormalization due to lattice mismatch in bilayer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:315502. [PMID: 38663420 DOI: 10.1088/1361-648x/ad43a3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 04/25/2024] [Indexed: 05/08/2024]
Abstract
We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.
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Affiliation(s)
- Xingchuan Zhu
- Interdisciplinary Center for Fundamental and Frontier Sciences, Nanjing University of Science and Technology, Jiangyin, Jiangsu 214443, People's Republic of China
| | - Junsong Sun
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Huaiming Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
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8
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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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Yu J, Foutty BA, Kwan YH, Barber ME, Watanabe K, Taniguchi T, Shen ZX, Parameswaran SA, Feldman BE. Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene. Nat Commun 2023; 14:6679. [PMID: 37865663 PMCID: PMC10590429 DOI: 10.1038/s41467-023-42275-6] [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: 05/26/2023] [Accepted: 10/05/2023] [Indexed: 10/23/2023] Open
Abstract
The flat electronic bands in magic-angle twisted bilayer graphene (MATBG) host a variety of correlated insulating ground states, many of which are predicted to support charged excitations with topologically non-trivial spin and/or valley skyrmion textures. However, it has remained challenging to experimentally address their ground state order and excitations, both because some of the proposed states do not couple directly to experimental probes, and because they are highly sensitive to spatial inhomogeneities in real samples. Here, using a scanning single-electron transistor, we observe thermodynamic gaps at even integer moiré filling factors at low magnetic fields. We find evidence of a field-tuned crossover from charged spin skyrmions to bare particle-like excitations, suggesting that the underlying ground state belongs to the manifold of strong-coupling insulators. From the spatial dependence of these states and the chemical potential variation within the flat bands, we infer a link between the stability of the correlated ground states and local twist angle and strain. Our work advances the microscopic understanding of the correlated insulators in MATBG and their unconventional excitations.
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Affiliation(s)
- Jiachen Yu
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory of Advanced Materials, Stanford, CA, 94305, USA
| | - Benjamin A Foutty
- Geballe Laboratory of Advanced Materials, Stanford, CA, 94305, USA
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
| | - Yves H Kwan
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, UK
| | - Mark E Barber
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory of Advanced Materials, Stanford, CA, 94305, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Zhi-Xun Shen
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory of Advanced Materials, Stanford, CA, 94305, USA
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | | | - Benjamin E Feldman
- Geballe Laboratory of Advanced Materials, Stanford, CA, 94305, USA.
- Department of Physics, Stanford University, Stanford, CA, 94305, USA.
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA.
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10
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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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11
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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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12
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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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13
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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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14
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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: 3] [Impact Index Per Article: 3.0] [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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15
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Sankar S, Sela E, Han C. Measuring Topological Entanglement Entropy Using Maxwell Relations. PHYSICAL REVIEW LETTERS 2023; 131:016601. [PMID: 37478453 DOI: 10.1103/physrevlett.131.016601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Accepted: 06/08/2023] [Indexed: 07/23/2023]
Abstract
Topological entanglement entropy (TEE) is a key diagnostic of topological order, allowing one to detect the presence of Abelian or non-Abelian anyons. However, there are currently no experimentally feasible protocols to measure TEE in condensed matter systems. Here, we propose a scheme to measure the TEE of chiral topological phases, carrying protected edge states, based on a nontrivial connection with the thermodynamic entropy change occurring in a quantum point contact (QPC) as it pinches off the topological liquid into two. We show how this entropy change can be extracted using Maxwell relations from charge detection of a nearby quantum dot. We demonstrate this explicitly for the Abelian Laughlin states, using an exact solution of the sine-Gordon model describing the universal crossover in the QPC. Our approach might open a new thermodynamic detection scheme of topological states also with non-Abelian statistics.
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Affiliation(s)
- Sarath Sankar
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Eran Sela
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Cheolhee Han
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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16
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Aggarwal D, Narula R, Ghosh S. A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:143001. [PMID: 36745922 DOI: 10.1088/1361-648x/acb984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 02/06/2023] [Indexed: 06/18/2023]
Abstract
The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp2carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.
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Affiliation(s)
| | - Rohit Narula
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
| | - Sankalpa Ghosh
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
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17
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Pan G, Zhang X, Lu H, Li H, Chen BB, Sun K, Meng ZY. Thermodynamic Characteristic for a Correlated Flat-Band System with a Quantum Anomalous Hall Ground State. PHYSICAL REVIEW LETTERS 2023; 130:016401. [PMID: 36669223 DOI: 10.1103/physrevlett.130.016401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
While the ground-state phase diagram of the correlated flat-band systems has been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance, and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, in chiral limit there exists a unique thermodynamic characteristic for the correlated flat-band model with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which transfers the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and gives rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.
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Affiliation(s)
- Gaopei Pan
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xu Zhang
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Hongyu Lu
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Heqiu Li
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Bin-Bin Chen
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
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18
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Child T, Sheekey O, Lüscher S, Fallahi S, Gardner GC, Manfra M, Mitchell A, Sela E, Kleeorin Y, Meir Y, Folk J. Entropy Measurement of a Strongly Coupled Quantum Dot. PHYSICAL REVIEW LETTERS 2022; 129:227702. [PMID: 36493429 DOI: 10.1103/physrevlett.129.227702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Accepted: 10/28/2022] [Indexed: 06/17/2023]
Abstract
The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.
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Affiliation(s)
- Timothy Child
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T1Z1, Canada
| | - Owen Sheekey
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T1Z1, Canada
| | - Silvia Lüscher
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T1Z1, Canada
| | - Saeed Fallahi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Geoffrey C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Andrew Mitchell
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
- Centre for Quantum Engineering, Science, and Technology, University College Dublin, Dublin 4, Ireland
| | - Eran Sela
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, IL-69978 Tel Aviv, Israel
| | - Yaakov Kleeorin
- Center for the Physics of Evolving Systems, University of Chicago, Chicago, Illinois 60637, USA
| | - Yigal Meir
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
- The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Joshua Folk
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T1Z1, Canada
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19
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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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20
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Wang G, Chen C, Beshiwork BA, Xu B, Dong Y, Lin B. Fast proton and water transport in ceramic membrane-based magic-angle graphene. WATER RESEARCH 2022; 225:119076. [PMID: 36155004 DOI: 10.1016/j.watres.2022.119076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 08/26/2022] [Accepted: 09/06/2022] [Indexed: 06/16/2023]
Abstract
Ceramic membranes for energy conversion and storage devices are essential for becoming carbon neutral due to low cost and high stability, but limited by slow proton and water transport. Meanwhile magic-angle graphene with unconventional superconductivity ushers in a new era, properties research of which are in infant stage, urgently longing for specific applications. Herein, we investigate the ionic-conductivity and water-transport properties of ceramic membrane-based magic-angle graphene by choosing proton and water as a proof-of-concept for the first time, discover the twist-angle tuned proton conduction and water transport in ceramic membrane-based magic-angle graphene, demonstrate the faster proton and water transport in magic-angle graphene than that in graphene, and construct an efficient device of protonic ceramic membrane fuel cell based upon the new fast proton-conducting materials of magic-angle graphene. The proton conduction and water transport in magic-angle graphene can be easily tuned by the twist angle, explained by the corresponding potential energy surface. The smaller the twist angle is, and the faster the proton transport is. The protonic migration energy barrier in magic-angle graphene is lower by about 50% than that in graphene. Additionally, the water transport properties in magic-angle graphene can be improved by tuning twist angles. The electrode with magic-angle graphene can provide higher performance of protonic ceramic membrane fuel cells. The present work opens the specific application of ceramic membrane-based magic-angle graphene as new proton-conducting and water-transport materials in energy and environment.
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Affiliation(s)
- Guoqing Wang
- School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Chen Chen
- School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Bayu Admasu Beshiwork
- School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Bo Xu
- Department of Physics, Laboratory of Computational Materials Physics, Jiangxi Normal University, Nanchang 330022, China
| | - Yingchao Dong
- Key Laboratory of Industrial Ecology and Environmental Engineering (Ministry of Education, MOE), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China.
| | - Bin Lin
- School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
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21
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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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22
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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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23
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Li P, Hou S, Alharbi B, Wu Q, Chen Y, Zhou L, Gao T, Li R, Yang L, Chang X, Dong G, Liu X, Decurtins S, Liu SX, Hong W, Lambert CJ, Jia C, Guo X. Quantum Interference-Controlled Conductance Enhancement in Stacked Graphene-like Dimers. J Am Chem Soc 2022; 144:15689-15697. [PMID: 35930760 DOI: 10.1021/jacs.2c05909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Stacking interactions are of significant importance in the fields of chemistry, biology, and material optoelectronics because they determine the efficiency of charge transfer between molecules and their quantum states. Previous studies have proven that when two monomers are π-stacked in series to form a dimer, the electrical conductance of the dimer is significantly lower than that of the monomer. Here, we present a strong opposite case that when two anthanthrene monomers are π-stacked to form a dimer in a scanning tunneling microscopic break junction, the conductance increases by as much as 25 in comparison with a monomer, which originates from a room-temperature quantum interference. Remarkably, both theory and experiment consistently reveal that this effect can be reversed by changing the connectivity of external electrodes to the monomer core. These results demonstrate that synthetic control of connectivity to molecular cores can be combined with stacking interactions between their π systems to modify and optimize charge transfer between molecules, opening up a wide variety of potential applications ranging from organic optoelectronics and photovoltaics to nanoelectronics and single-molecule electronics.
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Affiliation(s)
- Peihui Li
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China
| | - Songjun Hou
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - Bader Alharbi
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK.,Department of Physics, Prince Sattam Bin Abdulaziz University, Alkharj 16278, Saudi Arabia
| | - Qingqing Wu
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - Yijian Chen
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China
| | - Li Zhou
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China
| | - Tengyang Gao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Ruihao Li
- State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Lan Yang
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China
| | - Xinyue Chang
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China
| | - Gang Dong
- State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Xunshan Liu
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.,Department of Chemistry, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China
| | - Silvio Decurtins
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - Shi-Xia Liu
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - Wenjing Hong
- State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Colin J Lambert
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - Chuancheng Jia
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China.,Beijing National Laboratory for Molecular Sciences, National Biomedical Imaging Center, College of Chemistry and Molecular Engineering, Peking University, 292 Chengfu Road, Haidian District, Beijing 100871, P. R. China
| | - Xuefeng Guo
- Center of Single-Molecule Sciences, Institute of Modern Optics, Frontiers Science Center for New Organic Matter, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, College of Electronic Information and Optical Engineering, Nankai University, 38 Tongyan Road, Jinnan District, Tianjin 300350, P. R. China.,Beijing National Laboratory for Molecular Sciences, National Biomedical Imaging Center, College of Chemistry and Molecular Engineering, Peking University, 292 Chengfu Road, Haidian District, Beijing 100871, P. R. China
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24
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Song ZD, Bernevig BA. Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem. PHYSICAL REVIEW LETTERS 2022; 129:047601. [PMID: 35939005 DOI: 10.1103/physrevlett.129.047601] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 05/04/2022] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological semimetallic conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f and c electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f electrons coupled to nearly free c electrons-we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries of Refs. [1-5] as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations [2,6,7], and the minima of the charge gap at the Γ_{M} point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG.
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Affiliation(s)
- Zhi-Da Song
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Department of Physics, Princeton University, Princeton, New Jersey 08544, 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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25
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Lin H, Zhang Z, Zhang H, Lin KT, Wen X, Liang Y, Fu Y, Lau AKT, Ma T, Qiu CW, Jia B. Engineering van der Waals Materials for Advanced Metaphotonics. Chem Rev 2022; 122:15204-15355. [PMID: 35749269 DOI: 10.1021/acs.chemrev.2c00048] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The outstanding chemical and physical properties of 2D materials, together with their atomically thin nature, make them ideal candidates for metaphotonic device integration and construction, which requires deep subwavelength light-matter interaction to achieve optical functionalities beyond conventional optical phenomena observed in naturally available materials. In addition to their intrinsic properties, the possibility to further manipulate the properties of 2D materials via chemical or physical engineering dramatically enhances their capability, evoking new science on light-matter interaction, leading to leaped performance of existing functional devices and giving birth to new metaphotonic devices that were unattainable previously. Comprehensive understanding of the intrinsic properties of 2D materials, approaches and capabilities for chemical and physical engineering methods, the resulting property modifications and novel functionalities, and applications of metaphotonic devices are provided in this review. Through reviewing the detailed progress in each aspect and the state-of-the-art achievement, insightful analyses of the outstanding challenges and future directions are elucidated in this cross-disciplinary comprehensive review with the aim to provide an overall development picture in the field of 2D material metaphotonics and promote rapid progress in this fast emerging and prosperous field.
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Affiliation(s)
- Han Lin
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia.,The Australian Research Council (ARC) Industrial Transformation Training, Centre in Surface Engineering for Advanced Materials (SEAM), Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
| | - Zhenfang Zhang
- School of Textile Science and Engineering, Xi'an Polytechnic University, Xi'an 710048, China
| | - Huihui Zhang
- Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Keng-Te Lin
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia
| | - Xiaoming Wen
- Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Yao Liang
- Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Yang Fu
- Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Alan Kin Tak Lau
- Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Tianyi Ma
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia.,Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Baohua Jia
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia.,The Australian Research Council (ARC) Industrial Transformation Training, Centre in Surface Engineering for Advanced Materials (SEAM), Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.,Centre for Translational Atomaterials, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
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26
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Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene. Nat Commun 2022; 13:3292. [PMID: 35672329 PMCID: PMC9174269 DOI: 10.1038/s41467-022-30998-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 05/20/2022] [Indexed: 12/02/2022] Open
Abstract
New phase of matter usually emerges when a given symmetry breaks spontaneously, which can involve charge, spin, and valley degree of freedoms. Here, we report an observation of new correlated insulators evolved from spin-polarized states to valley-polarized states in twisted double bilayer graphene (TDBG) driven by the displacement field (D). At a high field |D | > 0.7 V/nm, we observe valley polarized correlated insulators with a big Zeeman g factor of ~10, both at v = 2 in the moiré conduction band and more surprisingly at v = −2 in the moiré valence band. Moreover, we observe a valley polarized Chern insulator with C = 2 emanating at v = 2 in the electron side and a valley polarized Fermi surface around v = −2 in the hole side. Our results demonstrate a feasible way to realize isospin control and to obtain new phases of matter in TDBG by the displacement field, and might benefit other twisted or non-twisted multilayer systems. Previous studies of twisted double bilayer graphene have been limited to AB-AB stacking, featuring spin-polarized correlated insulators. Here, the authors fabricate AB-BA devices and report a competition between spin and valley polarization, along with the emergence of valley-polarized correlated insulators tuned by electric field.
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27
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Das I, Shen C, Jaoui A, Herzog-Arbeitman J, Chew A, Cho CW, Watanabe K, Taniguchi T, Piot BA, Bernevig BA, Efetov DK. Observation of Reentrant Correlated Insulators and Interaction-Driven Fermi-Surface Reconstructions at One Magnetic Flux Quantum per Moiré Unit Cell in Magic-Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2022; 128:217701. [PMID: 35687461 DOI: 10.1103/physrevlett.128.217701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 03/30/2022] [Indexed: 06/15/2023]
Abstract
The discovery of flat bands with nontrivial band topology in magic-angle twisted bilayer graphene (MATBG) has provided a unique platform to study strongly correlated phenomena including superconductivity, correlated insulators, Chern insulators, and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hofstadter spectrum. Here, we report on a detailed magnetotransport study of a MATBG device in external magnetic fields of up to B=31 T, corresponding to one magnetic flux quantum per moiré unit cell Φ_{0}. At Φ_{0}, we observe reentrant correlated insulators at a flat band filling factors of ν=+2 and of ν=+3, and interaction-driven Fermi-surface reconstructions at other fillings, which are identified by new sets of Landau levels originating from these. These experimental observations are supplemented by theoretical work that predicts a new set of eight well-isolated flat bands at Φ_{0}, of comparable band width, but with different topology than in zero field. Overall, our magnetotransport data reveal a qualitatively new Hofstadter spectrum in MATBG, which arises due to the strong electronic correlations in the reentrant flat bands.
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Affiliation(s)
- Ipsita Das
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Cheng Shen
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Alexandre Jaoui
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | | | - Aaron Chew
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Chang-Woo Cho
- Laboratoire National des Champs Magnétiques Intenses, Université Grenoble Alpes, UPS-INSA-EMFL-CNRS-LNCMI, 25 avenue des Martyrs, 38042 Grenoble, France
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Benjamin A Piot
- Laboratoire National des Champs Magnétiques Intenses, Université Grenoble Alpes, UPS-INSA-EMFL-CNRS-LNCMI, 25 avenue des Martyrs, 38042 Grenoble, France
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Dmitri K Efetov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
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28
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Lin X, Chen BB, Li W, Meng ZY, Shi T. Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model. PHYSICAL REVIEW LETTERS 2022; 128:157201. [PMID: 35499872 DOI: 10.1103/physrevlett.128.157201] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Revised: 01/03/2022] [Accepted: 03/20/2022] [Indexed: 05/10/2023]
Abstract
A topological Mott insulator (TMI) with spontaneous time-reversal symmetry breaking and nonzero Chern number has been discovered in a real-space effective model for twisted bilayer graphene (TBG) at 3/4 filling in the strong coupling limit [1]. However, the finite temperature properties of such a TMI state remain illusive. In this work, employing the state-of-the-art thermal tensor network and the perturbative field-theoretical approaches, we obtain the finite-T phase diagram and the dynamical properties of the TBG model. The phase diagram includes the quantum anomalous Hall and charge density wave phases at low T, and an Ising transition separating them from the high-T symmetric phases. Because of the proliferation of excitons-particle-hole bound states-the transitions take place at a significantly reduced temperature than the mean-field estimation. The exciton phase is accompanied with distinctive experimental signatures in such as in charge compressibilities and optical conductivities close to the transition. Our work explains the smearing of the many-electron state topology by proliferating excitons and opens an avenue for controlled many-body investigations on finite-temperature states in the TBG and other quantum moiré systems.
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Affiliation(s)
- Xiyue Lin
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijng 100049, China
| | - Bin-Bin Chen
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Wei Li
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Tao Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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29
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Wagner G, Kwan YH, Bultinck N, Simon SH, Parameswaran SA. Global Phase Diagram of the Normal State of Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2022; 128:156401. [PMID: 35499897 DOI: 10.1103/physrevlett.128.156401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 03/28/2022] [Indexed: 06/14/2023]
Abstract
We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the "cascade" physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.
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Affiliation(s)
- Glenn Wagner
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Yves H Kwan
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Nick Bultinck
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Physics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S A Parameswaran
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
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30
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Child T, Sheekey O, Lüscher S, Fallahi S, Gardner GC, Manfra M, Folk J. A Robust Protocol for Entropy Measurement in Mesoscopic Circuits. ENTROPY (BASEL, SWITZERLAND) 2022; 24:417. [PMID: 35327927 PMCID: PMC8948648 DOI: 10.3390/e24030417] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Revised: 03/11/2022] [Accepted: 03/13/2022] [Indexed: 02/01/2023]
Abstract
Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement.
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Affiliation(s)
- Timothy Child
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
| | - Owen Sheekey
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
| | - Silvia Lüscher
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
| | - Saeed Fallahi
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA; (S.F.); (M.M.)
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA;
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN 47907, USA
| | - Geoffrey C. Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA;
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Michael Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA; (S.F.); (M.M.)
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA;
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Joshua Folk
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
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31
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Tsai Y, Li Z, Hu S. Recent Progress of Atomic Layer Technology in Spintronics: Mechanism, Materials and Prospects. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:661. [PMID: 35214988 PMCID: PMC8880290 DOI: 10.3390/nano12040661] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 02/10/2022] [Accepted: 02/13/2022] [Indexed: 12/16/2022]
Abstract
The atomic layer technique is generating a lot of excitement and study due to its profound physics and enormous potential in device fabrication. This article reviews current developments in atomic layer technology for spintronics, including atomic layer deposition (ALD) and atomic layer etching (ALE). To begin, we introduce the main atomic layer deposition techniques. Then, in a brief review, we discuss ALE technology for insulators, semiconductors, metals, and newly created two-dimensional van der Waals materials. Additionally, we compare the critical factors learned from ALD to constructing ALE technology. Finally, we discuss the future prospects and challenges of atomic layer technology in the field of spinronics.
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Affiliation(s)
| | | | - Shaojie Hu
- Center for Spintronics and Quantum Systems, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China; (Y.T.); (Z.L.)
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32
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Ochoa H, Fernandes RM. Degradation of Phonons in Disordered Moiré Superlattices. PHYSICAL REVIEW LETTERS 2022; 128:065901. [PMID: 35213205 DOI: 10.1103/physrevlett.128.065901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Revised: 11/29/2021] [Accepted: 01/14/2022] [Indexed: 06/14/2023]
Abstract
The elastic collective modes of a moiré superlattice arise not from vibrations of a rigid crystal but from the relative displacement between the constituent layers. Despite their similarity to acoustic phonons, these modes, called phasons, are not protected by any conservation law. Here, we show that disorder in the relative orientation between the layers and thermal fluctuations associated with their sliding motion degrade the propagation of sound in the moiré superlattice. Specifically, the phason modes become overdamped at low energies and acquire a finite gap, which displays a universal dependence on the twist-angle variance. Thus, twist-angle inhomogeneity is manifested not only in the noninteracting electronic structure of moiré systems, but also in their phononlike modes. More broadly, our results have important implications for the electronic properties of twisted moiré systems that are sensitive to the electron-phonon coupling.
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Affiliation(s)
- Héctor Ochoa
- Donostia International Physics Center, 20018 Donostia-San, Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - Rafael M Fernandes
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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33
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Lin JX, Zhang YH, Morissette E, Wang Z, Liu S, Rhodes D, Watanabe K, Taniguchi T, Hone J, Li JIA. Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene. Science 2022; 375:437-441. [PMID: 34990215 DOI: 10.1126/science.abh2889] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Strong electron correlation and spin-orbit coupling (SOC) can have a profound influence on the electronic properties of materials. We examined their combined influence on a two-dimensional electronic system at the atomic interface between magic-angle twisted bilayer graphene and a tungsten diselenide crystal. We found that strong electron correlation within the moiré flatband stabilizes correlated insulating states at both quarter and half filling, and that SOC transforms these Mott-like insulators into ferromagnets, as evidenced by a robust anomalous Hall effect with hysteretic switching behavior. The coupling between spin and valley degrees of freedom could be demonstrated through control of the magnetic order with an in-plane magnetic field or a perpendicular electric field. Our findings establish an experimental knob to engineer topological properties of moiré bands in twisted bilayer graphene and related systems.
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Affiliation(s)
- Jiang-Xiazi Lin
- Department of Physics, Brown University, Providence, RI 02912, USA
| | - Ya-Hui Zhang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Erin Morissette
- Department of Physics, Brown University, Providence, RI 02912, USA
| | - Zhi Wang
- Department of Physics, Brown University, Providence, RI 02912, USA
| | - Song Liu
- Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA
| | - Daniel Rhodes
- Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA
| | - 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
| | - James Hone
- Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA
| | - J I A Li
- Department of Physics, Brown University, Providence, RI 02912, USA
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Liu M, Wang L, Yu G. Developing Graphene-Based Moiré Heterostructures for Twistronics. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2103170. [PMID: 34723434 PMCID: PMC8728823 DOI: 10.1002/advs.202103170] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Revised: 09/08/2021] [Indexed: 06/13/2023]
Abstract
Graphene-based moiré heterostructures are strongly correlated materials, and they are considered to be an effective platform to investigate the challenges of condensed matter physics. This is due to the distinct electronic properties that are unique to moiré superlattices and peculiar band structures. The increasing research on strongly correlated physics via graphene-based moiré heterostructures, especially unconventional superconductors, greatly promotes the development of condensed matter physics. Herein, the preparation methods of graphene-based moiré heterostructures on both in situ growth and assembling monolayer 2D materials are discussed. Methods to improve the quality of graphene and optimize the transfer process are presented to mitigate the limitations of low-quality graphene and damage caused by the transfer process during the fabrication of graphene-based moiré heterostructures. Then, the topological properties in various graphene-based moiré heterostructures are reviewed. Furthermore, recent advances regarding the factors that influence physical performances via a changing twist angle, the exertion of strain, and regulation of the dielectric environment are presented. Moreover, various unique physical properties in graphene-based moiré heterostructures are demonstrated. Finally, the challenges faced during the preparation and characterization of graphene-based moiré heterostructures are discussed. An outlook for the further development of moiré heterostructures is also presented.
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Affiliation(s)
- Mengya Liu
- School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijing100083P. R. China
- Beijing National Laboratory for Molecular SciencesCAS Research/Education Center for Excellence in Molecular SciencesInstitute of ChemistryChinese Academy of SciencesBeijing100190P. R. China
| | - Liping Wang
- School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijing100083P. R. China
| | - Gui Yu
- Beijing National Laboratory for Molecular SciencesCAS Research/Education Center for Excellence in Molecular SciencesInstitute of ChemistryChinese Academy of SciencesBeijing100190P. R. China
- School of Chemical SciencesUniversity of Chinese Academy of SciencesBeijing100049P. R. China
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Cha P, Patel AA, Kim EA. Strange Metals from Melting Correlated Insulators in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2021; 127:266601. [PMID: 35029498 DOI: 10.1103/physrevlett.127.266601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Revised: 09/24/2021] [Accepted: 11/01/2021] [Indexed: 06/14/2023]
Abstract
Even as the understanding of the mechanism behind correlated insulating states in magic-angle twisted bilayer graphene converges toward various kinds of spontaneous symmetry breaking, the metallic "normal state" above the insulating transition temperature remains mysterious, with its excessively high entropy and linear-in-temperature resistivity. In this Letter, we focus on the effects of fluctuations of the order parameters describing correlated insulating states at integer fillings of the low-energy flat bands on charge transport. Motivated by the observation of heterogeneity in the order-parameter landscape at zero magnetic field in certain samples, we conjecture the existence of frustrating extended-range interactions in an effective Ising model of the order parameters on a triangular lattice. The competition between short-distance ferromagnetic interactions and frustrating extended-range antiferromagnetic interactions leads to an emergent length scale that forms stripy mesoscale domains above the ordering transition. The gapless fluctuations of these heterogeneous configurations are found to be responsible for the linear-in-temperature resistivity as well as the enhanced low-temperature entropy. Our insights link experimentally observed linear-in-temperature resistivity and enhanced entropy to the strength of frustration or, equivalently, to the emergence of mesoscopic length scales characterizing order-parameter domains.
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Affiliation(s)
- Peter Cha
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Aavishkar A Patel
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Eun-Ah Kim
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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Shavit G, Berg E, Stern A, Oreg Y. Theory of Correlated Insulators and Superconductivity in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2021; 127:247703. [PMID: 34951791 DOI: 10.1103/physrevlett.127.247703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Accepted: 11/18/2021] [Indexed: 06/14/2023]
Abstract
We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at noninteger fillings. Adding a phonon-mediated intervalley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moiré systems, such as twisted trilayer graphene.
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Affiliation(s)
- Gal Shavit
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 2021; 600:240-245. [PMID: 34670267 DOI: 10.1038/s41586-021-04121-x] [Citation(s) in RCA: 60] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 10/11/2021] [Indexed: 11/08/2022]
Abstract
The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors1-4, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5,6. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature Tc are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap ΔT, which far exceeds the mean-field BCS ratio (with 2ΔT/kBTc ~ 25), and the gap ΔAR extracted from Andreev reflection spectroscopy (2ΔAR/kBTc ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.
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Chou YZ, Wu F, Sau JD, Das Sarma S. Correlation-Induced Triplet Pairing Superconductivity in Graphene-Based Moiré Systems. PHYSICAL REVIEW LETTERS 2021; 127:217001. [PMID: 34860110 DOI: 10.1103/physrevlett.127.217001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model of Dirac fermions with spin, valley, and sublattice degrees of freedom. We find that the f-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and nontopological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively to Dirac fermions for the triplet-pairing superconductivity in graphene-based moiré systems, which is fundamentally distinct from triplet superconductivity in ^{3}He and ferromagnetic superconductors.
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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
| | - Fengcheng Wu
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jay D Sau
- 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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Li T, Zhu J, Tang Y, Watanabe K, Taniguchi T, Elser V, Shan J, Mak KF. Charge-order-enhanced capacitance in semiconductor moiré superlattices. NATURE NANOTECHNOLOGY 2021; 16:1068-1072. [PMID: 34426680 DOI: 10.1038/s41565-021-00955-8] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 07/01/2021] [Indexed: 06/13/2023]
Abstract
Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena1-17. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems10-17. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe2/WS2 moiré superlattices. We observed a series of incompressible states for filling factors 0-8 and anomalously large capacitance in the intervening compressible regions. The anomalously large capacitance, which was nearly 60% above the device's geometrical capacitance, was most pronounced at small filling factors, below the melting temperature of the charge-ordered states, and for small sample-gate separation. It is a manifestation of the device-geometry-dependent Coulomb interaction between electrons and phase mixing of the charge-ordered states. Based on these results, we were able to extract the thermodynamic gap of the correlated insulating states and the device's electronic entropy and specific heat capacity. Our findings establish capacitance as a powerful probe of the correlated states in semiconductor moiré systems and demonstrate control of these states via sample-gate coupling.
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Affiliation(s)
- Tingxin Li
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA
| | - Jiacheng Zhu
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA
| | - Yanhao Tang
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | | | - Veit Elser
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA
| | - Jie Shan
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA.
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA.
- Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA.
| | - Kin Fai Mak
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA.
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA.
- Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA.
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Potasz P, Xie M, MacDonald AH. Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2021; 127:147203. [PMID: 34652208 DOI: 10.1103/physrevlett.127.147203] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Revised: 08/09/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moiré bands of magic angle twisted bilayer graphene. For moiré band filling 3>|ν|>2, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near |ν|=3, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of magic angle twisted bilayer graphene flat band correlations.
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Affiliation(s)
- Pawel Potasz
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA and Department of Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
| | - Ming Xie
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - A H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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