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Li H, Chen CZ, Jiang H, Xie XC. Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}. PHYSICAL REVIEW LETTERS 2021; 127:236402. [PMID: 34936771 DOI: 10.1103/physrevlett.127.236402] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 11/04/2021] [Indexed: 06/14/2023]
Abstract
In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠0) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed C=2 phase [Deng et al., Science 367, 895 (2020)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}Te_{4}. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with C=1. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a C=2 phase. Eventually, we present a phase diagram of a disordered MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.
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Affiliation(s)
- Hailong Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Chui-Zhen Chen
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Institute for Advanced Study, Soochow University, Suzhou 215006, China
| | - Hua Jiang
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Institute for Advanced Study, Soochow University, Suzhou 215006, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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Liu FH, Hsu CS, Chuang C, Woo TP, Huang LI, Lo ST, Fukuyama Y, Yang Y, Elmquist RE, Liang CT. Dirac fermion heating, current scaling, and direct insulator-quantum Hall transition in multilayer epitaxial graphene. NANOSCALE RESEARCH LETTERS 2013; 8:360. [PMID: 23968131 PMCID: PMC3765374 DOI: 10.1186/1556-276x-8-360] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2013] [Accepted: 08/12/2013] [Indexed: 06/02/2023]
Abstract
We have performed magnetotransport measurements on multilayer epitaxial graphene. By increasing the driving current I through our graphene devices while keeping the bath temperature fixed, we are able to study Dirac fermion heating and current scaling in such devices. Using zero-field resistivity as a self thermometer, we are able to determine the effective Dirac fermion temperature (TDF) at various driving currents. At zero field, it is found that TDF ∝ I≈1/2. Such results are consistent with electron heating in conventional two-dimensional systems in the plateau-plateau transition regime. With increasing magnetic field B, we observe an I-independent point in the measured longitudinal resistivity ρxx which is equivalent to the direct insulator-quantum Hall (I-QH) transition characterized by a temperature-independent point in ρxx. Together with recent experimental evidence for direct I-QH transition, our new data suggest that such a transition is a universal effect in graphene, albeit further studies are required to obtain a thorough understanding of such an effect.
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Affiliation(s)
- Fan-Hung Liu
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
| | - Chang-Shun Hsu
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
| | - Chiashain Chuang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Tak-Pong Woo
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Lung-I Huang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Shun-Tsung Lo
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
| | - Yasuhiro Fukuyama
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
| | - Yanfei Yang
- National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USA
| | - Randolph E Elmquist
- National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USA
| | - Chi-Te Liang
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
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Pallecchi E, Ridene M, Kazazis D, Lafont F, Schopfer F, Poirier W, Goerbig MO, Mailly D, Ouerghi A. Insulating to relativistic quantum Hall transition in disordered graphene. Sci Rep 2013. [PMCID: PMC3646355 DOI: 10.1038/srep01791] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.
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Chuang C, Lin LH, Aoki N, Ouchi T, Mahjoub AM, Woo TP, Bird JP, Ochiai Y, Lo ST, Liang CT. Experimental evidence for direct insulator-quantum Hall transition in multi-layer graphene. NANOSCALE RESEARCH LETTERS 2013; 8:214. [PMID: 23647579 PMCID: PMC3655881 DOI: 10.1186/1556-276x-8-214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/05/2013] [Accepted: 04/24/2013] [Indexed: 06/02/2023]
Abstract
We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity ρxx, which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility μq of our device. It is found that at the direct I-QH transition, μqBc ≈ 0.37 which is considerably smaller than 1. In contrast, at Bc, ρxx is close to the Hall resistivity ρxy, i.e., the classical mobility μBc is ≈ 1. Therefore, our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.
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Affiliation(s)
- Chiashain Chuang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
| | - Li-Hung Lin
- Department of Electrophysics, National Chiayi University, Chiayi 600, Taiwan
| | - Nobuyuki Aoki
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
| | - Takahiro Ouchi
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
| | - Akram M Mahjoub
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
| | - Tak-Pong Woo
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Jonathan P Bird
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
- Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14206-1500, USA
| | - Yuichi Ochiai
- Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan
| | - Shun-Tsung Lo
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
| | - Chi-Te Liang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan
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Huang TY, Liang CT, Chen YF, Simmons MY, Kim GH, Ritchie DA. Direct measurement of the spin gaps in a gated GaAs two-dimensional electron gas. NANOSCALE RESEARCH LETTERS 2013; 8:138. [PMID: 23522392 PMCID: PMC3626693 DOI: 10.1186/1556-276x-8-138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/12/2013] [Accepted: 03/09/2013] [Indexed: 06/02/2023]
Abstract
We have performed magnetotransport measurements on gated GaAs two-dimensional electron gases in which electrons are confined in a layer of the nanoscale. From the slopes of a pair of spin-split Landau levels (LLs) in the energy-magnetic field plane, we can perform direct measurements of the spin gap for different LLs. The measured g-factor g is greatly enhanced over its bulk value in GaAs (0.44) due to electron-electron (e-e) interactions. Our results suggest that both the spin gap and g determined from conventional activation energy studies can be very different from those obtained by direct measurements.
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Affiliation(s)
- Tsai-Yu Huang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Chi-Te Liang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Yang Fang Chen
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Michelle Y Simmons
- School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Gil-Ho Kim
- School of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
| | - David A Ritchie
- Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK
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