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Zhuo D, Zhou L, Zhao YF, Zhang R, Yan ZJ, Wang AG, Chan MHW, Liu CX, Chen CZ, Chang CZ. Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers. NANO LETTERS 2024; 24:6974-6980. [PMID: 38829211 DOI: 10.1021/acs.nanolett.4c01313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2024]
Abstract
The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple domains and then reconverges back to a single magnetic domain. The layer structure of the sample provides an external knob for adjusting the Chern number C of the QAH insulators. Here, we employ molecular beam epitaxy to grow magnetic topological insulator multilayers and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change ΔC. We find that critical exponents extracted for the plateau phase transitions with ΔC = 1 and ΔC = 3 in QAH insulators are nearly identical. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with ΔC = 1 and ΔC = 3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different ΔC in QAH insulators.
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Affiliation(s)
- Deyi Zhuo
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Lingjie Zhou
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Yi-Fan Zhao
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Ruoxi Zhang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Zi-Jie Yan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Annie G Wang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Moses H W Chan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Chui-Zhen Chen
- Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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Wang FJ, Xiao ZY, Queiroz R, Bernevig BA, Stern A, Song ZD. Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry. Nat Commun 2024; 15:3069. [PMID: 38594296 PMCID: PMC11003978 DOI: 10.1038/s41467-024-47467-2] [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: 08/09/2023] [Accepted: 03/28/2024] [Indexed: 04/11/2024] Open
Abstract
Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average C2zT, m, and C4zT and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups P m , P 2 ' , P 4 ' , and P 6 ' with and without spin-orbit coupling, most of which can support CMP.
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Affiliation(s)
- Fa-Jie Wang
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China
| | - Zhen-Yu Xiao
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China
| | - Raquel Queiroz
- Department of Physics, Columbia University, New York, NY, USA
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Zhi-Da Song
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China.
- Hefei National Laboratory, Hefei, 230088, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China.
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Chen R, Sun HP, Gu M, Hua CB, Liu Q, Lu HZ, Xie XC. Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators. Natl Sci Rev 2024; 11:nwac140. [PMID: 38264341 PMCID: PMC10804226 DOI: 10.1093/nsr/nwac140] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Revised: 07/05/2022] [Accepted: 07/07/2022] [Indexed: 01/25/2024] Open
Abstract
The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.
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Affiliation(s)
- Rui Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
| | - Hai-Peng Sun
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, Würzburg 97074, Germany
| | - Mingqiang Gu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
| | - Chun-Bo Hua
- School of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China
| | - Qihang Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen 518055, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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Qin F, Chen R, Lu HZ. Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:225001. [PMID: 35134789 DOI: 10.1088/1361-648x/ac530f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
In this work, we investigate the topological phase transitions in an effective model for a topological thin film with high-frequency pumping. In particular, our results show that the circularly polarized light can break the time-reversal symmetry and induce the quantum anomalous Hall insulator (QAHI) phase. Meanwhile, the bulk magnetic moment can also break the time-reversal symmetry. Therefore, it shows rich phase diagram by tuning the intensity of the light and the thickness of the thin film. Using the parameters fitted by experimental data, we give the topological phase diagram of the Cr-doped Bi2Se3thin film, showing that by modulating the strength of the polarized optical field in an experimentally accessible range, there are four different phases: the normal insulator phase, the time-reversal-symmetry-broken quantum spin Hall insulator phase, and two different QAHI phases with opposite Chern numbers. Comparing with the non-doped Bi2Se3, it is found that the interplay between the light and bulk magnetic moment separates the two different QAHI phases with opposite Chern numbers. The results show that an intrinsic magnetic topological insulator with high-frequency pumping is an ideal platform for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.
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Affiliation(s)
- Fang Qin
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, People's Republic of China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, People's Republic of China
- Department of Physics, National University of Singapore, 117542, Singapore
| | - Rui Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, People's Republic of China
- School of Physics, Southeast University, Nanjing 211189, People's Republic of China
- Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, People's Republic of China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, People's Republic of China
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Lv QX, Du YX, Liang ZT, Liu HZ, Liang JH, Chen LQ, Zhou LM, Zhang SC, Zhang DW, Ai BQ, Yan H, Zhu SL. Measurement of Spin Chern Numbers in Quantum Simulated Topological Insulators. PHYSICAL REVIEW LETTERS 2021; 127:136802. [PMID: 34623865 DOI: 10.1103/physrevlett.127.136802] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wave functions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are nonvanished.
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Affiliation(s)
- Qing-Xian Lv
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Yan-Xiong Du
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Zhen-Tao Liang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Hong-Zhi Liu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Jia-Hao Liang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Lin-Qing Chen
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Li-Ming Zhou
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Shan-Chao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
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Wu X, Xiao D, Chen CZ, Sun J, Zhang L, Chan MHW, Samarth N, Xie XC, Lin X, Chang CZ. Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator. Nat Commun 2020; 11:4532. [PMID: 32913228 PMCID: PMC7483742 DOI: 10.1038/s41467-020-18312-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 08/18/2020] [Indexed: 11/08/2022] Open
Abstract
The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker-Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.
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Affiliation(s)
- Xinyu Wu
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
| | - Di Xiao
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Chui-Zhen Chen
- Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou, 215006, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
| | - Ling Zhang
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Moses H W Chan
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Nitin Samarth
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - X C Xie
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing, 100871, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China.
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA.
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7
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Deng W, Huang X, Lu J, Peri V, Li F, Huber SD, Liu Z. Acoustic spin-Chern insulator induced by synthetic spin-orbit coupling with spin conservation breaking. Nat Commun 2020; 11:3227. [PMID: 32591512 PMCID: PMC7320166 DOI: 10.1038/s41467-020-17039-1] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 06/05/2020] [Indexed: 11/28/2022] Open
Abstract
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we construct a two-dimensional topological acoustic crystal induced by the synthetic spin-orbit coupling, a crucial ingredient of topological insulators, with spin non-conservation. Our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing “spin” Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. More importantly, we observe the spin flipping transport in an H-shaped device, demonstrating evidently the spin non-conservation of the boundary states. In acoustic systems, quantum spin Hall physics is rarely observed because the crucial ingredient spin-orbit coupling is missing. Here, the authors construct an acoustic crystal with synthetic spin-orbit coupling and observe gapless helical boundary states as well as spin flipping effect.
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Affiliation(s)
- Weiyin Deng
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, Guangdong, 510640, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, Guangdong, 510640, China
| | - Jiuyang Lu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, Guangdong, 510640, China
| | - Valerio Peri
- Institute for Theoretical Physics, ETH Zurich, Zürich, 8093, Switzerland
| | - Feng Li
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, Guangdong, 510640, China.
| | - Sebastian D Huber
- Institute for Theoretical Physics, ETH Zurich, Zürich, 8093, Switzerland
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan, 430072, China. .,Institute for Advanced Studies, Wuhan University, Wuhan, 430072, China.
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