1
|
Lu Z, Han T, Yao Y, Reddy AP, Yang J, Seo J, Watanabe K, Taniguchi T, Fu L, Ju L. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 2024; 626:759-764. [PMID: 38383622 DOI: 10.1038/s41586-023-07010-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 12/21/2023] [Indexed: 02/23/2024]
Abstract
The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.
Collapse
Affiliation(s)
- Zhengguang Lu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Tonghang Han
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yuxuan Yao
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Aidan P Reddy
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jixiang Yang
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Junseok Seo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Long Ju
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
| |
Collapse
|
2
|
Liu K, Zheng J, Sha Y, Lyu B, Li F, Park Y, Ren Y, Watanabe K, Taniguchi T, Jia J, Luo W, Shi Z, Jung J, Chen G. Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene. NATURE NANOTECHNOLOGY 2024; 19:188-195. [PMID: 37996516 DOI: 10.1038/s41565-023-01558-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 10/30/2023] [Indexed: 11/25/2023]
Abstract
Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon-polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin-valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.
Collapse
Affiliation(s)
- Kai Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Jian Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Yating Sha
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Bosai Lyu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Fengping Li
- Department of Physics, University of Seoul, Seoul, Korea
| | - Youngju Park
- Department of Physics, University of Seoul, Seoul, Korea
| | - Yulu Ren
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Jinfeng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Weidong Luo
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Zhiwen Shi
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, Korea.
- Department of Smart Cities, University of Seoul, Seoul, Korea.
| | - Guorui Chen
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
Hagymási I, Mohd Isa MS, Tajkov Z, Márity K, Oroszlány L, Koltai J, Alassaf A, Kun P, Kandrai K, Pálinkás A, Vancsó P, Tapasztó L, Nemes-Incze P. Observation of competing, correlated ground states in the flat band of rhombohedral graphite. SCIENCE ADVANCES 2022; 8:eabo6879. [PMID: 36054359 PMCID: PMC10848960 DOI: 10.1126/sciadv.abo6879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
In crystalline solids, the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in "magic angle" graphene layers. Much less explored is rhombohedral graphite (RG), perhaps the simplest and structurally most perfect condensed matter system to host a flat band protected by symmetry. By scanning tunneling microscopy, we map the flat band charge density of 8, 10, 14, and 17 layers and identify a domain structure emerging from a competition between a sublattice antiferromagnetic insulator and a gapless correlated paramagnet. Our density matrix renormalization group calculations explain the observed features and demonstrate that the correlations are fundamentally different from graphene-based magnetism identified until now, forming the ground state of a quantum magnet. Our work establishes RG as a platform to study many-body interactions beyond the mean-field approach, where quantum fluctuations and entanglement dominate.
Collapse
Affiliation(s)
- Imre Hagymási
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
- Wigner Research Centre for Physics, 1121 Budapest, Hungary
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Mohammad Syahid Mohd Isa
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - Zoltán Tajkov
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
- Department of Biological Physics, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
| | - Krisztián Márity
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - László Oroszlány
- Department of Physics of Complex Systems, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
- Budapest University of Technology and Economics, 1111 Budapest, Hungary
| | - János Koltai
- Department of Biological Physics, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
| | - Assem Alassaf
- Department of Physics of Complex Systems, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
| | - Péter Kun
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - Konrád Kandrai
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - András Pálinkás
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - Péter Vancsó
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - Levente Tapasztó
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| | - Péter Nemes-Incze
- Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
| |
Collapse
|
5
|
Lee Y, Che S, Velasco J, Gao X, Shi Y, Tran D, Baima J, Mauri F, Calandra M, Bockrath M, Lau CN. Gate-Tunable Magnetism and Giant Magnetoresistance in Suspended Rhombohedral-Stacked Few-Layer Graphene. NANO LETTERS 2022; 22:5094-5099. [PMID: 35715214 DOI: 10.1021/acs.nanolett.2c00466] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Conventionally, magnetism arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. It can also emerge in perfect lattices from nonmagnetic elements, such as that exemplified by the Stoner criterion. Here we report tunable magnetism in suspended rhombohedral-stacked few-layer graphene (r-FLG) devices with flat bands. At small doping levels (n ∼ 1011 cm-2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature and disappear at n > 1012 cm-2 or T > 5 K. These results are confirmed by first-principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms.
Collapse
Affiliation(s)
- Yongjin Lee
- Samsung Semiconductor R&D Center, Hwasung-si, Gyeonggi-do 17113, South Korea
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
- Advanced Device Research Lab, Semiconductor R&D Center, Samsung Electronics Co., Ltd, 1 amsungjeonja-ro, Hwaseong-si, Gyeonggi-do 17113, Korea
| | - Shi Che
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
| | - Jairo Velasco
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Xueshi Gao
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
| | - Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
| | - David Tran
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
| | - Jacopo Baima
- Sorbonne Université, CNRS, Institut des Nanosciences de Paris, UMR7588, F-75252 Paris, France
| | - Francesco Mauri
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Matteo Calandra
- Sorbonne Université, CNRS, Institut des Nanosciences de Paris, UMR7588, F-75252 Paris, France
- Department of Physics, University of Trento, Via Sommarive 14, 38123 Povo, Italy
- Graphene Labs, Fondazione Istituto Italiano di Tecnologia, Via Morego, I-16163 Genova, Italy
| | - Marc Bockrath
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
| | - Chun Ning Lau
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Tanaka M, Shimazaki Y, Borzenets IV, Watanabe K, Taniguchi T, Tarucha S, Yamamoto M. Charge Neutral Current Generation in a Spontaneous Quantum Hall Antiferromagnet. PHYSICAL REVIEW LETTERS 2021; 126:016801. [PMID: 33480769 DOI: 10.1103/physrevlett.126.016801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 10/12/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
The intrinsic Hall effect allows for the generation of a nondissipative charge neutral current, such as a pure spin current generated via the spin Hall effect. Breaking of the spatial inversion or time reversal symmetries, or the spin-orbit interaction is generally considered necessary for the generation of such a charge neutral current. Here, we challenge this general concept and present generation and detection of a charge neutral current in a centrosymmetric material with little spin-orbit interaction. We employ bilayer graphene, and find enhanced nonlocal transport in the quantum Hall antiferromagnetic state, where spontaneous symmetry breaking occurs due to the electronic correlation.
Collapse
Affiliation(s)
- Miuko Tanaka
- Department of Applied Physics, University of Tokyo, Tokyo, 113-8656, Japan
| | - Yuya Shimazaki
- Institute of Quantum Electronics, ETH Zurich, CH-8093, Zurich, Switzerland
| | | | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, 305-0044, Japan
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Wako, 351-0198, Japan
| | | |
Collapse
|
8
|
Shi Y, Xu S, Yang Y, Slizovskiy S, Morozov SV, Son SK, Ozdemir S, Mullan C, Barrier J, Yin J, Berdyugin AI, Piot BA, Taniguchi T, Watanabe K, Fal’ko VI, Novoselov KS, Geim AK, Mishchenko A. Electronic phase separation in multilayer rhombohedral graphite. Nature 2020; 584:210-214. [DOI: 10.1038/s41586-020-2568-2] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 05/05/2020] [Indexed: 11/09/2022]
|
9
|
Chen G, Sharpe AL, Fox EJ, Zhang YH, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 2020; 579:56-61. [DOI: 10.1038/s41586-020-2049-7] [Citation(s) in RCA: 273] [Impact Index Per Article: 68.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Accepted: 12/11/2019] [Indexed: 11/09/2022]
|
10
|
Chen G, Sharpe AL, Gallagher P, Rosen IT, Fox EJ, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Jung J, Shi Z, Goldhaber-Gordon D, Zhang Y, Wang F. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 2019; 572:215-219. [PMID: 31316203 DOI: 10.1038/s41567-018-0387-2] [Citation(s) in RCA: 165] [Impact Index Per Article: 33.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 05/09/2019] [Indexed: 05/27/2023]
Abstract
Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as described by the Hubbard model2-4. An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron-electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in 'magic angle' twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice5,6 where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity ('domes') emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron-electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model.
Collapse
Affiliation(s)
- Guorui Chen
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Aaron L Sharpe
- Department of Applied Physics, Stanford University, Stanford, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Patrick Gallagher
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Ilan T Rosen
- Department of Applied Physics, Stanford University, Stanford, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Eli J Fox
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- Department of Physics, Stanford University, Stanford, CA, USA
| | - Lili Jiang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Bosai Lyu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China
| | - Hongyuan Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | | | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, South Korea
| | - Zhiwen Shi
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China
| | - David Goldhaber-Gordon
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA.
- Department of Physics, Stanford University, Stanford, CA, USA.
| | - Yuanbo Zhang
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China.
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China.
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, China.
| | - Feng Wang
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Kavli Energy NanoSciences Institute at the University of California, Berkeley, CA, USA.
| |
Collapse
|
11
|
Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 2019; 572:215-219. [PMID: 31316203 DOI: 10.1038/s41586-019-1393-y] [Citation(s) in RCA: 169] [Impact Index Per Article: 33.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 05/09/2019] [Indexed: 11/08/2022]
Abstract
Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as described by the Hubbard model2-4. An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron-electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in 'magic angle' twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice5,6 where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity ('domes') emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron-electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model.
Collapse
|
12
|
Abstract
The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance [Formula: see text] is first quantized to [Formula: see text] at a small perpendicular magnetic field [Formula: see text], establishing the presence of four edge channels. As [Formula: see text] increases, [Formula: see text] first decreases to [Formula: see text], indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong [Formula: see text] limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.
Collapse
|
13
|
Yin LJ, Shi LJ, Li SY, Zhang Y, Guo ZH, He L. High-Magnetic-Field Tunneling Spectra of ABC-Stacked Trilayer Graphene on Graphite. PHYSICAL REVIEW LETTERS 2019; 122:146802. [PMID: 31050464 DOI: 10.1103/physrevlett.122.146802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2018] [Indexed: 06/09/2023]
Abstract
ABC-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the ABC-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields.
Collapse
Affiliation(s)
- Long-Jing Yin
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, China
- Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education & Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University, Changsha, 410082, China
| | - Li-Juan Shi
- Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education & Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University, Changsha, 410082, China
| | - Si-Yu Li
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, China
| | - Yu Zhang
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, China
| | - Zi-Han Guo
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, China
| | - Lin He
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, China
| |
Collapse
|
14
|
Nam Y, Ki DK, Soler-Delgado D, Morpurgo AF. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 2018; 362:324-328. [PMID: 30337406 DOI: 10.1126/science.aar6855] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Accepted: 08/28/2018] [Indexed: 12/24/2022]
Abstract
Suspended Bernal-stacked graphene multilayers up to an unexpectedly large thickness exhibit a broken-symmetry ground state whose origin remains to be understood. We show that a finite-temperature second-order phase transition occurs in multilayers whose critical temperature (T c) increases from 12 kelvins (K) in bilayers to 100 K in heptalayers. A comparison of the data with a phenomenological model inspired by a mean-field approach suggests that the transition is associated with the appearance of a self-consistent valley- and spin-dependent staggered potential that changes sign from one layer to the next, appearing at T c and increasing upon cooling. The systematic evolution with thickness of several measured quantities imposes constraints on any microscopic theory aiming to analyze the nature of electronic correlations in this system.
Collapse
Affiliation(s)
- Youngwoo Nam
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, Gyeongsang National University, Jinju-daero 501, Jinju-si, South Korea
| | - Dong-Keun Ki
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, The University of Hong Kong, Hong Kong, China
| | - David Soler-Delgado
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland
| | - Alberto F Morpurgo
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.
| |
Collapse
|
15
|
Datta B, Agarwal H, Samanta A, Ratnakar A, Watanabe K, Taniguchi T, Sensarma R, Deshmukh MM. Landau Level Diagram and the Continuous Rotational Symmetry Breaking in Trilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 121:056801. [PMID: 30118256 DOI: 10.1103/physrevlett.121.056801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Revised: 05/03/2018] [Indexed: 06/08/2023]
Abstract
The sequence of the zeroth Landau levels (LLs) between filling factors ν=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the nonuniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the nonuniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the continuous rotational to C_{3} symmetry by the trigonal warping.
Collapse
Affiliation(s)
- Biswajit Datta
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Hitesh Agarwal
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhisek Samanta
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Amulya Ratnakar
- Department of Physics, UM-DAE Centre for Excellence in Basic Sciences, Mumbai 400098, India
| | - 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
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Mandar M Deshmukh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| |
Collapse
|
16
|
Shi Y, Che S, Zhou K, Ge S, Pi Z, Espiritu T, Taniguchi T, Watanabe K, Barlas Y, Lake R, Lau CN. Tunable Lifshitz Transitions and Multiband Transport in Tetralayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:096802. [PMID: 29547315 DOI: 10.1103/physrevlett.120.096802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Indexed: 06/08/2023]
Abstract
As the Fermi level and band structure of two-dimensional materials are readily tunable, they constitute an ideal platform for exploring the Lifshitz transition, a change in the topology of a material's Fermi surface. Using tetralayer graphene that host two intersecting massive Dirac bands, we demonstrate multiple Lifshitz transitions and multiband transport, which manifest as a nonmonotonic dependence of conductivity on the charge density n and out-of-plane electric field D, anomalous quantum Hall sequences and Landau level crossings that evolve with n, D, and B.
Collapse
Affiliation(s)
- Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Shi Che
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Kuan Zhou
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Supeng Ge
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Ziqi Pi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Timothy Espiritu
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Yafis Barlas
- Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, California 92521, USA
| | - Roger Lake
- Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, California 92521, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| |
Collapse
|
17
|
Gonzalez-Arraga LA, Lado JL, Guinea F, San-Jose P. Electrically Controllable Magnetism in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2017; 119:107201. [PMID: 28949176 DOI: 10.1103/physrevlett.119.107201] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
Twisted graphene bilayers develop highly localized states around AA-stacked regions for small twist angles. We show that interaction effects may induce either an antiferromagnetic or a ferromagnetic (FM) polarization of said regions, depending on the electrical bias between layers. Remarkably, FM-polarized AA regions under bias develop spiral magnetic ordering, with a relative 120° misalignment between neighboring regions due to a frustrated antiferromagnetic exchange. This remarkable spiral magnetism emerges naturally without the need of spin-orbit coupling, and competes with the more conventional lattice-antiferromagnetic instability, which interestingly develops at smaller bias under weaker interactions than in monolayer graphene, due to Fermi velocity suppression. This rich and electrically controllable magnetism could turn twisted bilayer graphene into an ideal system to study frustrated magnetism in two dimensions.
Collapse
Affiliation(s)
| | - J L Lado
- QuantaLab, International Iberian Nanotechnology Laboratory (INL), Avenida Mestre Jose Veiga, 4715-330 Braga, Portugal
| | - Francisco Guinea
- IMDEA Nanociencia, Calle de Faraday, 9, Cantoblanco, 28049 Madrid, Spain
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Pablo San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain
| |
Collapse
|
18
|
Datta B, Dey S, Samanta A, Agarwal H, Borah A, Watanabe K, Taniguchi T, Sensarma R, Deshmukh MM. Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene. Nat Commun 2017; 8:14518. [PMID: 28216666 PMCID: PMC5321728 DOI: 10.1038/ncomms14518] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Accepted: 01/06/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum Hall effect provides a simple way to study the competition between single particle physics and electronic interaction. However, electronic interaction becomes important only in very clean graphene samples and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due to high mobility ∼500,000 cm2 V−1 s−1 in our device compared to previous studies, we find all symmetry broken states and that Landau-level gaps are enhanced by interactions; an aspect explained by our self-consistent Hartree–Fock calculations. Moreover, we observe hysteresis as a function of filling factor and spikes in the longitudinal resistance which, together, signal the formation of quantum Hall ferromagnetic states at low magnetic field. Few-layered graphene offers a powerful platform to investigate electronic interactions beyond the non-interacting electron picture approximation. Here, the authors report the signature of strong electronic interactions and quantum Hall ferromagnetism in trilayer graphene with ABA stacking.
Collapse
Affiliation(s)
- Biswajit Datta
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Santanu Dey
- Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhisek Samanta
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Hitesh Agarwal
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhinandan Borah
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Mandar M Deshmukh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| |
Collapse
|
19
|
Stepanov P, Barlas Y, Espiritu T, Che S, Watanabe K, Taniguchi T, Smirnov D, Lau CN. Tunable Symmetries of Integer and Fractional Quantum Hall Phases in Heterostructures with Multiple Dirac Bands. PHYSICAL REVIEW LETTERS 2016; 117:076807. [PMID: 27563989 DOI: 10.1103/physrevlett.117.076807] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2016] [Indexed: 06/06/2023]
Abstract
The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.
Collapse
Affiliation(s)
- Petr Stepanov
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Yafis Barlas
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Tim Espiritu
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Shi Che
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki Tsukuba, Ibaraki 305-0044, Japan
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| |
Collapse
|
20
|
Henni Y, Ojeda Collado HP, Nogajewski K, Molas MR, Usaj G, Balseiro CA, Orlita M, Potemski M, Faugeras C. Rhombohedral Multilayer Graphene: A Magneto-Raman Scattering Study. NANO LETTERS 2016; 16:3710-3716. [PMID: 27164265 DOI: 10.1021/acs.nanolett.6b01041] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Graphene layers are known to stack in two stable configurations, namely, ABA or ABC stacking, with drastically distinct electronic properties. Unlike the ABA stacking, little has been done to experimentally investigate the electronic properties of ABC graphene multilayers. Here, we report on the first magneto optical study of a large ABC domain in a graphene multilayer flake, with ABC sequences exceeding 17 graphene sheets. ABC-stacked multilayers can be fingerprinted with a characteristic electronic Raman scattering response, which persists even at room temperatures. Tracing the magnetic field evolution of the inter Landau level excitations from this domain gives strong evidence for the existence of a dispersionless electronic band near the Fermi level, characteristic of such stacking. Our findings present a simple yet powerful approach to probe ABC stacking in graphene multilayer flakes, where this highly degenerated band appears as an appealing candidate to host strongly correlated states.
Collapse
Affiliation(s)
- Younes Henni
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| | - Hector Pablo Ojeda Collado
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica , 8400 S. C. de Bariloche, Argentina
| | - Karol Nogajewski
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| | - Maciej R Molas
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| | - Gonzalo Usaj
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica , 8400 S. C. de Bariloche, Argentina
| | - Carlos A Balseiro
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica , 8400 S. C. de Bariloche, Argentina
| | - Milan Orlita
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| | - Marek Potemski
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| | - Clement Faugeras
- LNCMI (CNRS, UJF, UPS, INSA), BP 166, 38042 Grenoble, Cedex 9, France
| |
Collapse
|
21
|
Yan J, Xia J, Wang X, Liu L, Kuo JL, Tay BK, Chen S, Zhou W, Liu Z, Shen ZX. Stacking-Dependent Interlayer Coupling in Trilayer MoS₂ with Broken Inversion Symmetry. NANO LETTERS 2015; 15:8155-61. [PMID: 26565932 DOI: 10.1021/acs.nanolett.5b03597] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The stacking configuration in few-layer two-dimensional (2D) materials results in different structural symmetries and layer-to-layer interactions, and hence it provides a very useful parameter for tuning their electronic properties. For example, ABA-stacking trilayer graphene remains semimetallic similar to that of monolayer, while ABC-stacking is predicted to be a tunable band gap semiconductor under an external electric field. Such stacking dependence resulting from many-body interactions has recently been the focus of intense research activities. Here we demonstrate that few-layer MoS2 samples grown by chemical vapor deposition with different stacking configurations (AA, AB for bilayer; AAB, ABB, ABA, AAA for trilayer) exhibit distinct coupling phenomena in both photoluminescence and Raman spectra. By means of ultralow-frequency (ULF) Raman spectroscopy, we demonstrate that the evolution of interlayer interaction with various stacking configurations correlates strongly with layer-breathing mode (LBM) vibrations. Our ab initio calculations reveal that the layer-dependent properties arise from both the spin-orbit coupling (SOC) and interlayer coupling in different structural symmetries. Such detailed understanding provides useful guidance for future spintronics fabrication using various stacked few-layer MoS2 blocks.
Collapse
Affiliation(s)
- Jiaxu Yan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
| | - Juan Xia
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
| | - Xingli Wang
- NOVITAS, Nanoelectronics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University , Singapore 639798, Singapore
| | - Lei Liu
- State Key Laboratory of Luminescence and Applications, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences , Changchun 130033, P. R. China
| | - Jer-Lai Kuo
- Institute of Atomic and Molecular Sciences, Academia Sinica , Taipei 10617, Taiwan
| | - Beng Kang Tay
- NOVITAS, Nanoelectronics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University , Singapore 639798, Singapore
| | - Shoushun Chen
- School of Electrical and Electronic Engineering, Nanyang Technological University , Singapore 639798, Singapore
| | - Wu Zhou
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Zheng Liu
- NOVITAS, Nanoelectronics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University , Singapore 639798, Singapore
- School of Materials Science and Engineering, Nanyang Technological University , Singapore 639798, Singapore
| | - Ze Xiang Shen
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University , Singapore 637371, Singapore
| |
Collapse
|
22
|
Khodkov T, Khrapach I, Craciun MF, Russo S. Direct Observation of a Gate Tunable Band Gap in Electrical Transport in ABC-Trilayer Graphene. NANO LETTERS 2015; 15:4429-4433. [PMID: 26079989 DOI: 10.1021/acs.nanolett.5b00772] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Few layer graphene systems such as Bernal stacked bilayer and rhombohedral (ABC-) stacked trilayer offer the unique possibility to open an electric field tunable energy gap. To date, this energy gap has been experimentally confirmed in optical spectroscopy. Here we report the first direct observation of the electric field tunable energy gap in electronic transport experiments on doubly gated suspended ABC-trilayer graphene. From a systematic study of the nonlinearities in current versus voltage characteristics and the temperature dependence of the conductivity, we demonstrate that thermally activated transport over the energy-gap dominates the electrical response of these transistors. The estimated values for energy gap from the temperature dependence and from the current voltage characteristics follow the theoretically expected electric field dependence with critical exponent 3/2. These experiments indicate that high quality few-layer graphene are suitable candidates for exploring novel tunable terahertz light sources and detectors.
Collapse
Affiliation(s)
- Tymofiy Khodkov
- Centre for Graphene Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Ivan Khrapach
- Centre for Graphene Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Monica Felicia Craciun
- Centre for Graphene Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Saverio Russo
- Centre for Graphene Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| |
Collapse
|
23
|
Competing ordered states with filling factor two in bilayer graphene. Nat Commun 2014; 5:4550. [DOI: 10.1038/ncomms5550] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2014] [Accepted: 06/27/2014] [Indexed: 11/09/2022] Open
|