Colloquium: Quantum anomalous Hall effect

Chang, Cui-Zu; Liu, Chao-Xing; MacDonald, Allan H.

doi:10.1103/revmodphys.95.011002

Title: Colloquium: Quantum anomalous Hall effect

Journal Article · Mon Jan 23 00:00:00 EST 2023 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/revmodphys.95.011002· OSTI ID:1968228

^[1]; Liu, Chao-Xing ^[1]; MacDonald, Allan H. ^[2]

Pennsylvania State Univ., University Park, PA (United States)
Univ. of Texas, Austin, TX (United States)

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators—topologically nontrivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, nontrivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. Here, the quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the (Bi,Sb)₂T₃ family, (ii) thin films of the intrinsic magnetic topological insulator MnBi₂Te₄, (iii) moiré materials formed from graphene, and (iv) moiré materials formed from transition-metal dichalcogenides. In this Colloquium, the physical mechanisms responsible for each class of QAH insulator are reviewed, with both differences and commonalities highlighted, and potential applications of the QAH effect are commented upon.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Army Research Office (ARO); NSF-MRSEC; US Air Force Office of Scientific Research (AFOSR); Gordon and Betty Moore Foundation’s EPiQS Initiative

Grant/Contract Number:: SC0022106; SC0023113; SC0019064; SC0019481; DMR-2011839; DMR-2011750; W911NF1810198; W911NF2210159; FA9550-21-1-0177; GBMF9063; DMR-1847811

OSTI ID:: 1968228

Alternate ID(s):: OSTI ID: 1968946

Journal Information:: Reviews of Modern Physics, Vol. 95, Issue 1; ISSN 0034-6861

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (413)

Nonlocal sidewall response and deviation from exact quantization of the topological magnetoelectric effect in axion-insulator thin films Pournaghavi, N.; Pertsova, A.; MacDonald, A. H. Physical Review B, Vol. 104, Issue 20 https://doi.org/10.1103/PhysRevB.104.L201102	journal	November 2021
Tunable and sizable band gap of single-layer graphene sandwiched between hexagonal boron nitride Quhe, Ruge; Zheng, Jiaxin; Luo, Guangfu NPG Asia Materials, Vol. 4, Issue 2 https://doi.org/10.1038/am.2012.10	journal	February 2012
Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition Wang, Jing; Zhou, Quan; Lian, Biao Physical Review B, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevB.92.064520	journal	August 2015
Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing Xiong, Gang; Wang, Shi-Dong; Niu, Qian Physical Review Letters, Vol. 87, Issue 21 https://doi.org/10.1103/PhysRevLett.87.216802	journal	November 2001
Landau Quantization and the Thickness Limit of Topological Insulator Thin Films of ${Sb}_{2} {Te}_{3}$ Jiang, Yeping; Wang, Yilin; Chen, Mu Physical Review Letters, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevLett.108.016401	journal	January 2012
Intrinsic quantized anomalous Hall effect in a moiré heterostructure Serlin, M.; Tschirhart, C. L.; Polshyn, H. Science, Vol. 367, Issue 6480 https://doi.org/10.1126/science.aay5533	journal	December 2019
Comparing magnetic ground-state properties of the V- and Cr-doped topological insulator ${(Bi, Sb)}_{2} {Te}_{3}$ Tcakaev, A.; Zabolotnyy, V. B.; Green, R. J. Physical Review B, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevB.101.045127	journal	January 2020
Current-induced breakdown of the quantum anomalous Hall effect Lippertz, Gertjan; Bliesener, Andrea; Uday, Anjana Physical Review B, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevB.106.045419	journal	July 2022
Direct evidence of ferromagnetism in ${MnSb}_{2} {Te}_{4}$ Ge, Wenbo; Sass, Paul M.; Yan, Jiaqiang Physical Review B, Vol. 103, Issue 13 https://doi.org/10.1103/PhysRevB.103.134403	journal	April 2021
Intrinsic quantum anomalous Hall phase induced by proximity in the van der Waals heterostructure germanene/ ${Cr}_{2} {Ge}_{2} {Te}_{6}$ Zou, Runling; Zhan, Fangyang; Zheng, Baobing Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.161108	journal	April 2020
Experimental Realization of a Three-Dimensional Topological Insulator, Bi₂Te₃ Chen, Y. L.; Analytis, J. G.; Chu, J.-H. Science, Vol. 325, Issue 5937, p. 178-181 https://doi.org/10.1126/science.1173034	journal	June 2009
Gapless Dirac surface states in the antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$ Swatek, Przemyslaw; Wu, Yun; Wang, Lin-Lin Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.161109	journal	April 2020
Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy Connolly, M. R.; Puddy, R. K.; Logoteta, D. Nano Letters, Vol. 12, Issue 11 https://doi.org/10.1021/nl3015395	journal	October 2012
Origins of electronic bands in the antiferromagnetic topological insulator MnBi2Te4 Yan, Chenhui; Fernandez-Mulligan, Sebastian; Mei, Ruobing Physical Review B, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevB.104.L041102	journal	July 2021
Delocalization Transition of a Disordered Axion Insulator Song, Zhi-Da; Lian, Biao; Queiroz, Raquel Physical Review Letters, Vol. 127, Issue 1 https://doi.org/10.1103/PhysRevLett.127.016602	journal	June 2021
Antiferromagnetism. Theory of Superexchange Interaction Anderson, P. W. Physical Review, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRev.79.350	journal	July 1950
Heavy Dirac fermions in a graphene/topological insulator hetero-junction Cao, Wendong; Zhang, Rui-Xing; Tang, Peizhe 2D Materials, Vol. 3, Issue 3 https://doi.org/10.1088/2053-1583/3/3/034006	journal	September 2016
Enhancing the Quantum Anomalous Hall Effect by Magnetic Codoping in a Topological Insulator Ou, Yunbo; Liu, Chang; Jiang, Gaoyuan Advanced Materials, Vol. 30, Issue 1 https://doi.org/10.1002/adma.201703062	journal	November 2017
Demonstration of Dissipative Quasihelical Edge Transport in Quantum Anomalous Hall Insulators Wang, Shu-Wei; Xiao, Di; Dou, Ziwei Physical Review Letters, Vol. 125, Issue 12 https://doi.org/10.1103/PhysRevLett.125.126801	journal	September 2020
Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene Wu, Fengcheng; Das Sarma, Sankar Physical Review Letters, Vol. 124, Issue 4 https://doi.org/10.1103/PhysRevLett.124.046403	journal	January 2020
Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors Qi, Xiao-Liang; Wu, Yong-Shi; Zhang, Shou-Cheng Physical Review B, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevB.74.085308	journal	August 2006
The electronic properties of graphene Castro Neto, A. H.; Guinea, F.; Peres, N. M. R. Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162 https://doi.org/10.1103/RevModPhys.81.109	journal	January 2009
Theory of the Dirac half metal and quantum anomalous Hall effect in Mn-intercalated epitaxial graphene Li, Yuanchang; West, Damien; Huang, Huaqing Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.201403	journal	November 2015
Graphene bilayers with a twist Andrei, Eva Y.; MacDonald, Allan H. Nature Materials, Vol. 19, Issue 12 https://doi.org/10.1038/s41563-020-00840-0	journal	November 2020
Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet ${MnBi}_{2} {Te}_{4}$ Films Otrokov, M. M.; Rusinov, I. P.; Blanco-Rey, M. Physical Review Letters, Vol. 122, Issue 10 https://doi.org/10.1103/PhysRevLett.122.107202	journal	March 2019
Universal gapless Dirac cone and tunable topological states in ${(MnB i_{2} T e_{4})}_{m} {(B i_{2} T e_{3})}_{n}$ heterostructures Hu, Yong; Xu, Lixuan; Shi, Mengzhu Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.161113	journal	April 2020
Routes to realize the axion-insulator phase in MnBi₂Te₄(Bi₂Te₃)_n family Zhao, Yufei; Liu, Qihang Applied Physics Letters, Vol. 119, Issue 6 https://doi.org/10.1063/5.0059447	journal	August 2021
Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator Liu, Chang; Wang, Yongchao; Yang, Ming Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-25002-x	journal	July 2021
Magnetic Weyl semimetal phase in a Kagomé crystal Liu, D. F.; Liang, A. J.; Liu, E. K. Science, Vol. 365, Issue 6459 https://doi.org/10.1126/science.aav2873	journal	September 2019
Modern theory of orbital magnetic moment in solids Aryasetiawan, F.; Karlsson, K. Journal of Physics and Chemistry of Solids, Vol. 128 https://doi.org/10.1016/j.jpcs.2017.12.004	journal	May 2019
Fractional Chern insulators in magic-angle twisted bilayer graphene Xie, Yonglong; Pierce, Andrew T.; Park, Jeong Min Nature, Vol. 600, Issue 7889 https://doi.org/10.1038/s41586-021-04002-3	journal	December 2021
Strong Spin-Orbit Splitting on Bi Surfaces Koroteev, Yu. M.; Bihlmayer, G.; Gayone, J. E. Physical Review Letters, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevLett.93.046403	journal	July 2004
Topological insulators with inversion symmetry Fu, Liang; Kane, C. L. Physical Review B, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevB.76.045302	journal	July 2007
In-plane magnetic field induced density wave states near quantum spin Hall phase transitions Zeng, Yongxin; Xue, Fei; MacDonald, Allan H. Physical Review B, Vol. 105, Issue 12 https://doi.org/10.1103/PhysRevB.105.125102	journal	March 2022
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Theory of the Three-Dimensional Quantum Hall Effect in Graphite Bernevig, B. Andrei; Hughes, Taylor L.; Raghu, Srinivas Physical Review Letters, Vol. 99, Issue 14 https://doi.org/10.1103/PhysRevLett.99.146804	journal	October 2007
Quantum Spin Hall Effect in Inverted Type-II Semiconductors Liu, Chaoxing; Hughes, Taylor L.; Qi, Xiao-Liang Physical Review Letters, Vol. 100, Issue 23 https://doi.org/10.1103/PhysRevLett.100.236601	journal	June 2008
Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride Shi, Jingtian; Zhu, Jihang; MacDonald, A. H. Physical Review B, Vol. 103, Issue 7 https://doi.org/10.1103/PhysRevB.103.075122	journal	February 2021
Precise resistance measurement of quantum anomalous Hall effect in magnetic heterostructure film of topological insulator Okazaki, Yuma; Oe, Takehiko; Kawamura, Minoru Applied Physics Letters, Vol. 116, Issue 14 https://doi.org/10.1063/1.5145172	journal	April 2020
Physical Realization of the Parity Anomaly in Condensed Matter Physics Fradkin, Eduardo; Dagotto, Elbio; Boyanovsky, Daniel Physical Review Letters, Vol. 57, Issue 23 https://doi.org/10.1103/PhysRevLett.57.2967	journal	December 1986
Interplay of Exciton Condensation and the Quantum Spin Hall Effect in $InAs / GaSb$ Bilayers Pikulin, D. I.; Hyart, T. Physical Review Letters, Vol. 112, Issue 17 https://doi.org/10.1103/PhysRevLett.112.176403	journal	April 2014
Quantum Anomalous Hall Effect in Magnetically Doped InAs/GaSb Quantum Wells Wang, Qing-Ze; Liu, Xin; Zhang, Hai-Jun Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.147201	journal	September 2014
Experimental Observation of the Gate-Controlled Reversal of the Anomalous Hall Effect in the Intrinsic Magnetic Topological Insulator MnBi ₂ Te ₄ Device Zhang, Shuai; Wang, Rui; Wang, Xuepeng Nano Letters, Vol. 20, Issue 1 https://doi.org/10.1021/acs.nanolett.9b04555	journal	December 2019
Tuning the Chern number in quantum anomalous Hall insulators Zhao, Yi-Fan; Zhang, Ruoxi; Mei, Ruobing Nature, Vol. 588, Issue 7838 https://doi.org/10.1038/s41586-020-3020-3	journal	December 2020
Symmetry-enforced chiral hinge states and surface quantum anomalous Hall effect in the magnetic axion insulator Bi2–xSmxSe3 Yue, Changming; Xu, Yuanfeng; Song, Zhida Nature Physics, Vol. 15, Issue 6 https://doi.org/10.1038/s41567-019-0457-0	journal	March 2019
Topological Materials: Quantum Anomalous Hall System He, Ke; Wang, Yayu; Xue, Qi-Kun Annual Review of Condensed Matter Physics, Vol. 9, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-054144	journal	March 2018
Prediction and observation of an antiferromagnetic topological insulator Otrokov, M. M.; Klimovskikh, I. I.; Bentmann, H. Nature, Vol. 576, Issue 7787 https://doi.org/10.1038/s41586-019-1840-9	journal	December 2019
Magnetic Properties of Cu-Mn Alloys Yosida, Kei Physical Review, Vol. 106, Issue 5 https://doi.org/10.1103/PhysRev.106.893	journal	June 1957
Antiferromagnetic topological insulator MnBi ₂ Te ₄ : synthesis and magnetic properties Li, Hao; Liu, Shengsheng; Liu, Chang Physical Chemistry Chemical Physics, Vol. 22, Issue 2 https://doi.org/10.1039/C9CP05634C	journal	January 2020
Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands Kang, Jian; Vafek, Oskar Physical Review Letters, Vol. 122, Issue 24 https://doi.org/10.1103/PhysRevLett.122.246401	journal	June 2019
Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle Seo, Kangjun; Kotov, Valeri N.; Uchoa, Bruno Physical Review Letters, Vol. 122, Issue 24 https://doi.org/10.1103/PhysRevLett.122.246402	journal	June 2019
Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ Lee, Seng Huat; Graf, David; Min, Lujin Physical Review X, Vol. 11, Issue 3 https://doi.org/10.1103/PhysRevX.11.031032	journal	August 2021
High-temperature intrinsic quantum anomalous Hall effect in rare Earth monohalide Wu, Menghao 2D Materials, Vol. 4, Issue 2 https://doi.org/10.1088/2053-1583/aa5c63	journal	February 2017
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields Hofstadter, Douglas R. Physical Review B, Vol. 14, Issue 6 https://doi.org/10.1103/PhysRevB.14.2239	journal	September 1976
Quantized Anomalous Hall Effect in Magnetic Topological Insulators Yu, R.; Zhang, W.; Zhang, H. -J. Science, Vol. 329, Issue 5987 https://doi.org/10.1126/science.1187485	journal	June 2010
Models of Exchange Coupling in Ferromagnetic Media Van Vleck, J. H. Reviews of Modern Physics, Vol. 25, Issue 1 https://doi.org/10.1103/RevModPhys.25.220	journal	January 1953
Evidence for Majorana bound states in an iron-based superconductor Wang, Dongfei; Kong, Lingyuan; Fan, Peng Science, Vol. 362, Issue 6412 https://doi.org/10.1126/science.aao1797	journal	August 2018
Axion electrodynamics in topological materials Sekine, Akihiko; Nomura, Kentaro Journal of Applied Physics, Vol. 129, Issue 14 https://doi.org/10.1063/5.0038804	journal	April 2021
Pseudospin magnetism in graphene Min, Hongki; Borghi, Giovanni; Polini, Marco Physical Review B, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevB.77.041407	journal	January 2008
Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator ${MnBi}_{2} {Te}_{4}$ Hao, Yu-Jie; Liu, Pengfei; Feng, Yue Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041038	journal	November 2019
Dirac Surface States in Intrinsic Magnetic Topological Insulators EuSn 2 As 2 and MnBi 2 n Te 3 n + 1 Li, Hang; Gao, Shun-Ye; Duan, Shao-Feng Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041039	journal	November 2019
Site Mixing for Engineering Magnetic Topological Insulators Liu, Yaohua; Wang, Lin-Lin; Zheng, Qiang Physical Review X, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevX.11.021033	journal	May 2021
Topological response of the anomalous Hall effect in MnBi2Te4 due to magnetic canting Bac, S. -K.; Koller, K.; Lux, F. npj Quantum Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41535-022-00455-5	journal	April 2022
Quantum Spin Hall Insulator State in HgTe Quantum Wells Konig, M.; Wiedmann, S.; Brune, C. Science, Vol. 318, Issue 5851, p. 766-770 https://doi.org/10.1126/science.1148047	journal	November 2007
Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening Liu, Xiaoxue; Wang, Zhi; Watanabe, K. Science, Vol. 371, Issue 6535 https://doi.org/10.1126/science.abb8754	journal	March 2021
3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals Wang, C. M.; Sun, Hai-Peng; Lu, Hai-Zhou Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.136806	journal	September 2017
Time-Reversal Symmetry-Breaking Nematic Insulators near Quantum Spin Hall Phase Transitions Xue, Fei; MacDonald, A. H. Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/PhysRevLett.120.186802	journal	May 2018
Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle Ahn, Junyeong; Park, Sungjoon; Yang, Bohm-Jung Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021013	journal	April 2019
Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi 2 Te 4 Chen, Y. J.; Xu, L. X.; Li, J. H. Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041040	journal	November 2019
Site mixing induced ferrimagnetism and anomalous transport properties of the Weyl semimetal candidate MnSb2Te4 Yan, D. Y.; Yang, M.; Song, P. B. Physical Review B, Vol. 103, Issue 22 https://doi.org/10.1103/PhysRevB.103.224412	journal	June 2021
Even–Odd Layer-Dependent Anomalous Hall Effect in Topological Magnet MnBi ₂ Te ₄ Thin Films Zhao, Yi-Fan; Zhou, Ling-Jie; Wang, Fei Nano Letters, Vol. 21, Issue 18 https://doi.org/10.1021/acs.nanolett.1c02493	journal	September 2021
Critical Behavior and Universal Signature of an Axion Insulator State Li, Hailong; Jiang, Hua; Chen, Chui-Zhen Physical Review Letters, Vol. 126, Issue 15 https://doi.org/10.1103/PhysRevLett.126.156601	journal	April 2021
Pseudospin order in monolayer, bilayer and double-layer graphene MacDonald, A. H.; Jung, Jeil; Zhang, Fan Physica Scripta, Vol. T146 https://doi.org/10.1088/0031-8949/2012/T146/014012	journal	January 2012
Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator Liu, Minhao; Wang, Wudi; Richardella, Anthony R. Science Advances, Vol. 2, Issue 7 https://doi.org/10.1126/sciadv.1600167	journal	July 2016
Quantum Theory of Orbital Magnetization and Its Generalization to Interacting Systems Shi, Junren; Vignale, G.; Xiao, Di Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.197202	journal	November 2007
Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator Wang, Fei; Xiao, Di; Yuan, Wei Nano Letters, Vol. 19, Issue 5 https://doi.org/10.1021/acs.nanolett.9b00027	journal	March 2019
Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene Saito, Yu; Ge, Jingyuan; Rademaker, Louk Nature Physics, Vol. 17, Issue 4 https://doi.org/10.1038/s41567-020-01129-4	journal	January 2021
Growth and transport properties of Sb2−xVxTe3 thin films on sapphire substrates Chien, Yi-Jiunn; Zhou, Zhenhua; Uher, Ctirad Journal of Crystal Growth, Vol. 283, Issue 3-4 https://doi.org/10.1016/j.jcrysgro.2005.06.046	journal	October 2005
Quantum anomalous Hall effect in stable dumbbell stanene Zhang, Huisheng; Zhang, Jiayong; Zhao, Bao Applied Physics Letters, Vol. 108, Issue 8 https://doi.org/10.1063/1.4942193	journal	February 2016
Possible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field Halperin, Bertrand I. Japanese Journal of Applied Physics, Vol. 26, Issue S3-3 https://doi.org/10.7567/JJAPS.26S3.1913	journal	January 1987
Nuclear Spin Exchange in Solids: ${Tl}^{203}$ and ${Tl}^{205}$ Magnetic Resonance in Thallium and Thallic Oxide Bloembergen, N.; Rowland, T. J. Physical Review, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRev.97.1679	journal	March 1955
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang, C. -Z.; Zhang, J.; Feng, X. Science, Vol. 340, Issue 6129 https://doi.org/10.1126/science.1234414	journal	March 2013
Theory of ferromagnetic (III,Mn)V semiconductors Jungwirth, T.; Sinova, Jairo; Mašek, J. Reviews of Modern Physics, Vol. 78, Issue 3 https://doi.org/10.1103/RevModPhys.78.809	journal	August 2006
Quantum Anomalous Hall Effect in 2D Organic Topological Insulators Wang, Z. F.; Liu, Zheng; Liu, Feng Physical Review Letters, Vol. 110, Issue 19 https://doi.org/10.1103/PhysRevLett.110.196801	journal	May 2013
Möbius Insulator and Higher-Order Topology in ${MnBi}_{2 n} {Te}_{3 n + 1}$ Zhang, Rui-Xing; Wu, Fengcheng; Das Sarma, S. Physical Review Letters, Vol. 124, Issue 13 https://doi.org/10.1103/PhysRevLett.124.136407	journal	April 2020
Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling Högl, Petra; Frank, Tobias; Zollner, Klaus Physical Review Letters, Vol. 124, Issue 13 https://doi.org/10.1103/PhysRevLett.124.136403	journal	March 2020
Correlated insulating states at fractional fillings of moiré superlattices Xu, Yang; Liu, Song; Rhodes, Daniel A. Nature, Vol. 587, Issue 7833 https://doi.org/10.1038/s41586-020-2868-6	journal	November 2020
Emerging chiral edge states from the confinement of a magnetic Weyl semimetal in ${Co}_{3} {Sn}_{2} S_{2}$ Muechler, Lukas; Liu, Enke; Gayles, Jacob Physical Review B, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevB.101.115106	journal	March 2020
Functionalized bismuth films: Giant gap quantum spin Hall and valley-polarized quantum anomalous Hall states Niu, Chengwang; Bihlmayer, Gustav; Zhang, Hongbin Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.041303	journal	January 2015
Orbital Magnetization as a Local Property Bianco, Raffaello; Resta, Raffaele Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/PhysRevLett.110.087202	journal	February 2013
Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures Jiang, Jue; Xiao, Di; Wang, Fei Nature Materials, Vol. 19, Issue 7 https://doi.org/10.1038/s41563-020-0605-z	journal	February 2020
Crystal growth and magnetic structure of ${MnBi}_{2} {Te}_{4}$ Yan, J. -Q.; Zhang, Q.; Heitmann, T. Physical Review Materials, Vol. 3, Issue 6 https://doi.org/10.1103/PhysRevMaterials.3.064202	journal	June 2019
Machine learning enabled autonomous microstructural characterization in 3D samples Chan, Henry; Cherukara, Mathew; Loeffler, Troy D. npj Computational Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41524-019-0267-z	journal	January 2020
Crossover from 2D Ferromagnetic Insulator to Wide Band Gap Quantum Anomalous Hall Insulator in Ultrathin MnBi ₂ Te ₄ Trang, Chi Xuan; Li, Qile; Yin, Yuefeng ACS Nano, Vol. 15, Issue 8 https://doi.org/10.1021/acsnano.1c03936	journal	August 2021
Thin film dilute ferromagnetic semiconductors ${Sb}_{2 - x} {Cr}_{x} {Te}_{3}$ with a Curie temperature up to $190 K$ Zhou, Zhenhua; Chien, Yi-Jiunn; Uher, Ctirad Physical Review B, Vol. 74, Issue 22 https://doi.org/10.1103/PhysRevB.74.224418	journal	December 2006
Realization of quantum anomalous Hall effect in graphene from $n - p$ codoping-induced stable atomic adsorption Deng, Xinzhou; Qi, Shifei; Han, Yulei Physical Review B, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevB.95.121410	journal	March 2017
Quantum Spin Hall Effect Bernevig, B. Andrei; Zhang, Shou-Cheng Physical Review Letters, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevLett.96.106802	journal	March 2006
Topological Electronic Structure and Intrinsic Magnetization in ${MnBi}_{4} {Te}_{7}$ : A ${Bi}_{2} {Te}_{3}$ Derivative with a Periodic Mn Sublattice Vidal, Raphael C.; Zeugner, Alexander; Facio, Jorge I. Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041065	journal	December 2019
Higher-Order Topology of the Axion Insulator ${EuIn}_{2} {As}_{2}$ Xu, Yuanfeng; Song, Zhida; Wang, Zhijun Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.256402	journal	June 2019
Scaling theory of the integer quantum Hall effect Huckestein, Bodo Reviews of Modern Physics, Vol. 67, Issue 2 https://doi.org/10.1103/RevModPhys.67.357	journal	April 1995
Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 122, Issue 8 https://doi.org/10.1103/PhysRevLett.122.086402	journal	February 2019
Theory of quantised Hall conductivity in two dimensions Streda, P. Journal of Physics C: Solid State Physics, Vol. 15, Issue 22 https://doi.org/10.1088/0022-3719/15/22/005	journal	August 1982
Topological Spin Texture in a Quantum Anomalous Hall Insulator Wu, Jiansheng; Liu, Jie; Liu, Xiong-Jun Physical Review Letters, Vol. 113, Issue 13 https://doi.org/10.1103/PhysRevLett.113.136403	journal	September 2014
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031089	journal	September 2018
Quantum Valley Hall Effect, Orbital Magnetism, and Anomalous Hall Effect in Twisted Multilayer Graphene Systems Liu, Jianpeng; Ma, Zhen; Gao, Jinhua Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031021	journal	August 2019
3D quantum Hall effect Lu, Hai-Zhou National Science Review, Vol. 6, Issue 2 https://doi.org/10.1093/nsr/nwy082	journal	August 2018
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
Transport properties of thin flakes of the antiferromagnetic topological insulator $MnB i_{2} T e_{4}$ Cui, Jianhua; Shi, Mengzhu; Wang, Honghui Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155125	journal	April 2019
Influence of the dissipative topological edge state on quantized transport in MnBi2Te4 Lin, Weiyan; Feng, Yang; Wang, Yongchao Physical Review B, Vol. 105, Issue 16 https://doi.org/10.1103/PhysRevB.105.165411	journal	April 2022
Odd-Even Layer-Number Effect and Layer-Dependent Magnetic Phase Diagrams in ${MnBi}_{2} {Te}_{4}$ Yang, Shiqi; Xu, Xiaolong; Zhu, Yaozheng Physical Review X, Vol. 11, Issue 1 https://doi.org/10.1103/PhysRevX.11.011003	journal	January 2021
Chiral topological superconductor from the quantum Hall state Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 82, Issue 18 https://doi.org/10.1103/PhysRevB.82.184516	journal	November 2010
Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co ₃ Sn ₂ S ₂ Morali, Noam; Batabyal, Rajib; Nag, Pranab Kumar Science, Vol. 365, Issue 6459 https://doi.org/10.1126/science.aav2334	journal	September 2019
Possible realization of the high-temperature and multichannel quantum anomalous Hall effect in graphene/CrBr 3 heterostructures under pressure Zhang, Huisheng; Ning, Yaohui; Yang, Wenjia Physical Chemistry Chemical Physics, Vol. 21, Issue 31 https://doi.org/10.1039/C9CP03219C	journal	January 2019
Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states Allen, Monica; Cui, Yongtao; Yue Ma, Eric Proceedings of the National Academy of Sciences, Vol. 116, Issue 29 https://doi.org/10.1073/pnas.1818255116	journal	July 2019
Spin-orbit–driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene Lin, Jiang-Xiazi; Zhang, Ya-Hui; Morissette, Erin Science, Vol. 375, Issue 6579 https://doi.org/10.1126/science.abh2889	journal	January 2022
Quantum anomalous Hall and quantum spin-Hall phases in flattened Bi and Sb bilayers Jin, Kyung-Hwan; Jhi, Seung-Hoon Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep08426	journal	February 2015
Recent advancements in the study of intrinsic magnetic topological insulators and magnetic Weyl semimetals Ning, Wei; Mao, Zhiqiang APL Materials, Vol. 8, Issue 9 https://doi.org/10.1063/5.0015328	journal	September 2020
Thin Films of Magnetically Doped Topological Insulator with Carrier-Independent Long-Range Ferromagnetic Order Chang, Cui-Zu; Zhang, Jinsong; Liu, Minhao Advanced Materials, Vol. 25, Issue 7 https://doi.org/10.1002/adma.201203493	journal	January 2013
Chern Semimetal and the Quantized Anomalous Hall Effect in ${HgCr}_{2} {Se}_{4}$ Xu, Gang; Weng, Hongming; Wang, Zhijun Physical Review Letters, Vol. 107, Issue 18 https://doi.org/10.1103/PhysRevLett.107.186806	journal	October 2011
Magnetized topological insulator multilayers Lei, Chao; Chen, Shu; MacDonald, Allan H. Proceedings of the National Academy of Sciences, Vol. 117, Issue 44 https://doi.org/10.1073/pnas.2014004117	journal	October 2020
Surface edge state and half-quantized Hall conductance in topological insulators Chu, Rui-Lin; Shi, Junren; Shen, Shun-Qing Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085312	journal	August 2011
Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons Ruderman, M. A.; Kittel, C. Physical Review, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRev.96.99	journal	October 1954
Valley-Polarized Quantum Anomalous Hall State in Moiré ${MoTe}_{2} / {WSe}_{2}$ Heterobilayers Xie, Ying-Ming; Zhang, Cheng-Ping; Hu, Jin-Xin Physical Review Letters, Vol. 128, Issue 2 https://doi.org/10.1103/PhysRevLett.128.026402	journal	January 2022
Tunable 3D/2D magnetism in the (MnBi2Te4)(Bi2Te3)m topological insulators family Klimovskikh, Ilya I.; Otrokov, Mikhail M.; Estyunin, Dmitry npj Quantum Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41535-020-00255-9	journal	August 2020
Experimental evidence for dissipationless transport of the chiral edge state of the high-field Chern insulator in MnBi2Te4 nanodevices Ying, Zhe; Zhang, Shuai; Chen, Bo Physical Review B, Vol. 105, Issue 8 https://doi.org/10.1103/PhysRevB.105.085412	journal	February 2022
Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect in Magnetically Disordered Topological Insulators Nomura, Kentaro; Nagaosa, Naoto Physical Review Letters, Vol. 106, Issue 16 https://doi.org/10.1103/PhysRevLett.106.166802	journal	April 2011
Intrinsic axion insulating behavior in antiferromagnetic ${MnBi}_{6} {Te}_{10}$ Jo, Na Hyun; Wang, Lin-Lin; Slager, Robert-Jan Physical Review B, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevB.102.045130	journal	July 2020
Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect Fox, E. J.; Rosen, I. T.; Yang, Yanfei Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevB.98.075145	journal	August 2018
Anomalous Hall effect Nagaosa, Naoto; Sinova, Jairo; Onoda, Shigeki Reviews of Modern Physics, Vol. 82, Issue 2 https://doi.org/10.1103/RevModPhys.82.1539	journal	May 2010
Observation of superparamagnetism in coexistence with quantum anomalous Hall C = ±1 and C = 0 Chern states Lachman, Ella O.; Mogi, Masataka; Sarkar, Jayanta npj Quantum Materials, Vol. 2, Issue 1 https://doi.org/10.1038/s41535-017-0072-1	journal	December 2017
Distinct Topological Surface States on the Two Terminations of ${MnBi}_{4} {Te}_{7}$ Wu, Xuefeng; Li, Jiayu; Ma, Xiao-Ming Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031013	journal	July 2020
Topological Mott Insulators Raghu, S.; Qi, Xiao-Liang; Honerkamp, C. Physical Review Letters, Vol. 100, Issue 15 https://doi.org/10.1103/PhysRevLett.100.156401	journal	April 2008
High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator Chang, Cui-Zu; Zhao, Weiwei; Kim, Duk Y. Nature Materials, Vol. 14, Issue 5 https://doi.org/10.1038/nmat4204	journal	March 2015
Chern Insulators from Heavy Atoms on Magnetic Substrates Garrity, Kevin F.; Vanderbilt, David Physical Review Letters, Vol. 110, Issue 11 https://doi.org/10.1103/PhysRevLett.110.116802	journal	March 2013
Quantum anomalous Hall effect in graphene from Rashba and exchange effects Qiao, Zhenhua; Yang, Shengyuan A.; Feng, Wanxiang Physical Review B, Vol. 82, Issue 16 https://doi.org/10.1103/PhysRevB.82.161414	journal	October 2010
Spin polarization in nanojunctions of quantum anomalous Hall insulators Cheraghchi, Hosein; Sabze, Tahere Journal of Magnetism and Magnetic Materials, Vol. 513 https://doi.org/10.1016/j.jmmm.2020.166923	journal	November 2020
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 185, Issue 1 https://doi.org/10.1016/0550-3213(81)90361-8	journal	July 1981
Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered ${MnBi}_{2} {Te}_{4}$ Li, Hailong; Chen, Chui-Zhen; Jiang, Hua Physical Review Letters, Vol. 127, Issue 23 https://doi.org/10.1103/PhysRevLett.127.236402	journal	December 2021
Distinct Quantum Anomalous Hall Ground States Induced by Magnetic Disorders Liu, Chang; Ou, Yunbo; Feng, Yang Physical Review X, Vol. 10, Issue 4 https://doi.org/10.1103/PhysRevX.10.041063	journal	December 2020
Electrically Tunable Quantum Anomalous Hall Effect in Graphene Decorated by $5 d$ Transition-Metal Adatoms Zhang, Hongbin; Lazo, Cesar; Blügel, Stefan Physical Review Letters, Vol. 108, Issue 5 https://doi.org/10.1103/PhysRevLett.108.056802	journal	February 2012
Experimental Realization of an Intrinsic Magnetic Topological Insulator ^* Gong, Yan; Guo, Jingwen; Li, Jiaheng Chinese Physics Letters, Vol. 36, Issue 7 https://doi.org/10.1088/0256-307X/36/7/076801	journal	June 2019
Visualization of superparamagnetic dynamics in magnetic topological insulators Lachman, Ella O.; Young, Andrea F.; Richardella, Anthony Science Advances, Vol. 1, Issue 10 https://doi.org/10.1126/sciadv.1500740	journal	November 2015
Precision measurement of the quantized anomalous Hall resistance at zero magnetic field Götz, Martin; Fijalkowski, Kajetan M.; Pesel, Eckart Applied Physics Letters, Vol. 112, Issue 7 https://doi.org/10.1063/1.5009718	journal	February 2018
The quantum Hall effect as an electrical resistance standard Jeckelmann, B.; Jeanneret, B. Reports on Progress in Physics, Vol. 64, Issue 12 https://doi.org/10.1088/0034-4885/64/12/201	journal	November 2001
A valley valve and electron beam splitter Li, Jing; Zhang, Rui-Xing; Yin, Zhenxi Science, Vol. 362, Issue 6419 https://doi.org/10.1126/science.aao5989	journal	December 2018
Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator Checkelsky, J. G.; Yoshimi, R.; Tsukazaki, A. Nature Physics, Vol. 10, Issue 10 https://doi.org/10.1038/nphys3053	journal	August 2014
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 98, Issue 10, Article No. 106803 https://doi.org/10.1103/PhysRevLett.98.106803	journal	March 2007
First-principles theory of dilute magnetic semiconductors Sato, K.; Bergqvist, L.; Kudrnovský, J. Reviews of Modern Physics, Vol. 82, Issue 2 https://doi.org/10.1103/RevModPhys.82.1633	journal	May 2010
Large-Gap Quantum Spin Hall Insulators in Tin Films Xu, Yong; Yan, Binghai; Zhang, Hai-Jun Physical Review Letters, Vol. 111, Issue 13 https://doi.org/10.1103/PhysRevLett.111.136804	journal	September 2013
Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer Zhu, Qizhong; Tu, Matisse Wei-Yuan; Tong, Qingjun Science Advances, Vol. 5, Issue 1 https://doi.org/10.1126/sciadv.aau6120	journal	January 2019
Magnetic Imaging of Domain Walls in the Antiferromagnetic Topological Insulator MnBi ₂ Te ₄ Sass, Paul M.; Ge, Wenbo; Yan, Jiaqiang Nano Letters, Vol. 20, Issue 4 https://doi.org/10.1021/acs.nanolett.0c00114	journal	March 2020
Exciton Band Topology in Spontaneous Quantum Anomalous Hall Insulators: Applications to Twisted Bilayer Graphene Kwan, Yves H.; Hu, Yichen; Simon, Steven H. Physical Review Letters, Vol. 126, Issue 13 https://doi.org/10.1103/PhysRevLett.126.137601	journal	March 2021
Quantum Anomalous Hall Effect and Tunable Topological States in 3d Transition Metals Doped Silicene Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep02908	journal	October 2013
Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene Pierce, Andrew T.; Xie, Yonglong; Park, Jeong Min Nature Physics, Vol. 17, Issue 11 https://doi.org/10.1038/s41567-021-01347-4	journal	September 2021
Evidence of Orbital Ferromagnetism in Twisted Bilayer Graphene Aligned to Hexagonal Boron Nitride Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W. Nano Letters, Vol. 21, Issue 10 https://doi.org/10.1021/acs.nanolett.1c00696	journal	May 2021
Exchange Interactions Zener, C.; Heikes, R. R. Reviews of Modern Physics, Vol. 25, Issue 1 https://doi.org/10.1103/RevModPhys.25.191.2	journal	January 1953
Ferromagnetism in van der Waals compound $MnS b_{1.8} B i_{0.2} T e_{4}$ Chen, Yangyang; Chuang, Ya-Wen; Lee, Seng Huat Physical Review Materials, Vol. 4, Issue 6 https://doi.org/10.1103/PhysRevMaterials.4.064411	journal	June 2020
Domain wall in a quantum anomalous Hall insulator as a magnetoelectric piston Upadhyaya, Pramey; Tserkovnyak, Yaroslav Physical Review B, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevB.94.020411	journal	July 2016
Theory of the Role of Covalence in the Perovskite-Type Manganites $[La, M (II)] Mn O_{3}$ Goodenough, John B. Physical Review, Vol. 100, Issue 2 https://doi.org/10.1103/PhysRev.100.564	journal	October 1955
Prediction of Near-Room-Temperature Quantum Anomalous Hall Effect on Honeycomb Materials Wu, Shu-Chun; Shan, Guangcun; Yan, Binghai Physical Review Letters, Vol. 113, Issue 25 https://doi.org/10.1103/PhysRevLett.113.256401	journal	December 2014
Coupled Spin and Valley Physics in Monolayers of ${MoS}_{2}$ and Other Group-VI Dichalcogenides Xiao, Di; Liu, Gui-Bin; Feng, Wanxiang Physical Review Letters, Vol. 108, Issue 19 https://doi.org/10.1103/PhysRevLett.108.196802	journal	May 2012
Electronic fingerprints of Cr and V dopants in the topological insulator Sb2Te3 Zhang, Wenhan; West, Damien; Lee, Seng Huat Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115165	journal	September 2018
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators Mogi, Masataka; Nakajima, Taro; Ukleev, Victor Physical Review Letters, Vol. 123, Issue 1 https://doi.org/10.1103/PhysRevLett.123.016804	journal	July 2019
Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene Chen, Shaowen; He, Minhao; Zhang, Ya-Hui Nature Physics, Vol. 17, Issue 3 https://doi.org/10.1038/s41567-020-01062-6	journal	October 2020
Distinguishing a Majorana zero mode using spin-resolved measurements Jeon, Sangjun; Xie, Yonglong; Li, Jian Science, Vol. 358, Issue 6364 https://doi.org/10.1126/science.aan3670	journal	October 2017
Quantum anomalous Hall Majorana platform Zeng, Yongxin; Lei, Chao; Chaudhary, Gaurav Physical Review B, Vol. 97, Issue 8 https://doi.org/10.1103/PhysRevB.97.081102	journal	February 2018
Two-dimensional Weyl half-semimetal and tunable quantum anomalous Hall effect You, Jing-Yang; Chen, Cong; Zhang, Zhen Physical Review B, Vol. 100, Issue 6 https://doi.org/10.1103/PhysRevB.100.064408	journal	August 2019
Topological quantum phase transition in magnetic topological insulator upon magnetization rotation Kawamura, Minoru; Mogi, Masataka; Yoshimi, Ryutaro Physical Review B, Vol. 98, Issue 14 https://doi.org/10.1103/PhysRevB.98.140404	journal	October 2018
Theory of Orbital Magnetization in Solids Thonhauser, T. International Journal of Modern Physics B, Vol. 25, Issue 11 https://doi.org/10.1142/S0217979211058912	journal	April 2011
Robust quantum anomalous Hall effect in graphene-based van der Waals heterostructures Zhang, Jiayong; Zhao, Bao; Yao, Yugui Physical Review B, Vol. 92, Issue 16 https://doi.org/10.1103/PhysRevB.92.165418	journal	October 2015
Quantum anomalous Hall insulator phase in asymmetrically functionalized germanene Hsu, Chia-Hsiu; Fang, Yimei; Wu, Shunqing Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165426	journal	October 2017
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W. Science, Vol. 365, Issue 6453 https://doi.org/10.1126/science.aaw3780	journal	July 2019
Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator Wu, L.; Salehi, M.; Koirala, N. Science, Vol. 354, Issue 6316 https://doi.org/10.1126/science.aaf5541	journal	December 2016
Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit Kou, Xufeng; Guo, Shih-Ting; Fan, Yabin Physical Review Letters, Vol. 113, Issue 13 https://doi.org/10.1103/PhysRevLett.113.137201	journal	September 2014
Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state Wang, Jing; Lian, Biao; Qi, Xiao-Liang Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.081107	journal	August 2015
Electrical switching of magnetic order in an orbital Chern insulator Polshyn, H.; Zhu, J.; Kumar, M. A. Nature, Vol. 588, Issue 7836 https://doi.org/10.1038/s41586-020-2963-8	journal	November 2020
Imaging orbital ferromagnetism in a moiré Chern insulator Tschirhart, C. L.; Serlin, M.; Polshyn, H. Science, Vol. 372, Issue 6548 https://doi.org/10.1126/science.abd3190	journal	June 2021
Resistance metrology based on the quantum Hall effect Poirier, W.; Schopfer, F. The European Physical Journal Special Topics, Vol. 172, Issue 1 https://doi.org/10.1140/epjst/e2009-01051-5	journal	June 2009
Functionalization induced quantum spin Hall to quantum anomalous Hall phase transition in monolayer jacutingaite Luo, Fangxue; Hao, Xiamin; Jia, Yizhen Nanoscale, Vol. 13, Issue 4 https://doi.org/10.1039/D0NR06889F	journal	January 2021
Quantum anomalous Hall state in bilayer graphene Nandkishore, Rahul; Levitov, Leonid Physical Review B, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevB.82.115124	journal	September 2010
Quantum anomalous Hall effect in metal-bis(dithiolene), magnetic properties, doping and interfacing graphene Crasto de Lima, F.; Ferreira, Gerson J.; Miwa, R. H. Physical Chemistry Chemical Physics, Vol. 20, Issue 35 https://doi.org/10.1039/C8CP03792B	journal	January 2018
Intrinsic magnetic topological insulators Wang, Pinyuan; Ge, Jun; Li, Jiaheng The Innovation, Vol. 2, Issue 2 https://doi.org/10.1016/j.xinn.2021.100098	journal	May 2021
Quantized response and topology of magnetic insulators with inversion symmetry Turner, Ari M.; Zhang, Yi; Mong, Roger S. K. Physical Review B, Vol. 85, Issue 16 https://doi.org/10.1103/PhysRevB.85.165120	journal	April 2012
Universal scaling of the quantum anomalous Hall plateau transition Wang, Jing; Lian, Biao; Zhang, Shou-Cheng Physical Review B, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevB.89.085106	journal	February 2014
Surface states and Rashba-type spin polarization in antiferromagnetic MnBi 2 Te 4 (0001) Vidal, R. C.; Bentmann, H.; Peixoto, T. R. F. Physical Review B, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevB.100.121104	journal	September 2019
Quantized chiral edge conduction on domain walls of a magnetic topological insulator Yasuda, K.; Mogi, M.; Yoshimi, R. Science, Vol. 358, Issue 6368 https://doi.org/10.1126/science.aan5991	journal	December 2017
Nearly flat Chern bands in moiré superlattices Zhang, Ya-Hui; Mao, Dan; Cao, Yuan Physical Review B, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevB.99.075127	journal	February 2019
Quantized Hall Conductance in a Two-Dimensional Periodic Potential Thouless, D. J.; Kohmoto, M.; Nightingale, M. P. Physical Review Letters, Vol. 49, Issue 6 https://doi.org/10.1103/PhysRevLett.49.405	journal	August 1982
Spontaneous Quantum Hall States in Chirally Stacked Few-Layer Graphene Systems Zhang, Fan; Jung, Jeil; Fiete, Gregory A. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/PhysRevLett.106.156801	journal	April 2011
Chern insulator at a magnetic rocksalt interface Garrity, Kevin F.; Vanderbilt, David Physical Review B, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevB.90.121103	journal	September 2014
Synthesis, Magnetic Properties, and Electronic Structure of Magnetic Topological Insulator MnBi ₂ Se ₄ Zhu, Tiancong; Bishop, Alexander J.; Zhou, Tong Nano Letters, Vol. 21, Issue 12 https://doi.org/10.1021/acs.nanolett.1c00141	journal	June 2021
Valley-polarized quantum anomalous Hall phases and tunable topological phase transitions in half-hydrogenated Bi honeycomb monolayers Liu, Cheng-Cheng; Zhou, Jin-Jian; Yao, Yugui Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.165430	journal	April 2015
Gate-controlled topological conducting channels in bilayer graphene Li, Jing; Wang, Ke; McFaul, Kenton J. Nature Nanotechnology, Vol. 11, Issue 12 https://doi.org/10.1038/nnano.2016.158	journal	August 2016
Electric-field control of ferromagnetism Ohno, H.; Chiba, D.; Matsukura, F. Nature, Vol. 408, Issue 6815 https://doi.org/10.1038/35050040	journal	December 2000
Weyl Semimetal in a Topological Insulator Multilayer Burkov, A. A.; Balents, Leon Physical Review Letters, Vol. 107, Issue 12 https://doi.org/10.1103/PhysRevLett.107.127205	journal	September 2011
Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures Xiao, Di; Jiang, Jue; Shin, Jae-Ho Physical Review Letters, Vol. 120, Issue 5 https://doi.org/10.1103/PhysRevLett.120.056801	journal	January 2018
Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator Feng, Yang; Feng, Xiao; Ou, Yunbo Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.126801	journal	September 2015
Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet Belopolski, Ilya; Manna, Kaustuv; Sanchez, Daniel S. Science, Vol. 365, Issue 6459 https://doi.org/10.1126/science.aav2327	journal	September 2019
Observation of the universal magnetoelectric effect in a 3D topological insulator Dziom, V.; Shuvaev, A.; Pimenov, A. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15197	journal	May 2017
Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state Grauer, S.; Schreyeck, S.; Winnerlein, M. Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.201304	journal	November 2015
Anomalous Edge Transport in the Quantum Anomalous Hall State Wang, Jing; Lian, Biao; Zhang, Haijun Physical Review Letters, Vol. 111, Issue 8 https://doi.org/10.1103/PhysRevLett.111.086803	journal	August 2013
Electronic States and Magnetic Response of MnBi ₂ Te ₄ by Scanning Tunneling Microscopy and Spectroscopy Yuan, Yonghao; Wang, Xintong; Li, Hao Nano Letters, Vol. 20, Issue 5 https://doi.org/10.1021/acs.nanolett.0c00031	journal	April 2020
Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure Watanabe, R.; Yoshimi, R.; Kawamura, M. Applied Physics Letters, Vol. 115, Issue 10 https://doi.org/10.1063/1.5111891	journal	September 2019
Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects Otrokov, M. M.; Menshchikova, T. V.; Vergniory, M. G. 2D Materials, Vol. 4, Issue 2 https://doi.org/10.1088/2053-1583/aa6bec	journal	April 2017
Mapping Dirac fermions in the intrinsic antiferromagnetic topological insulators $(Mn {Bi}_{2} {Te}_{4}) {({Bi}_{2} {Te}_{3})}_{n}$ ( $n = 0, 1$ ) Liang, Zuowei; Luo, Aiyun; Shi, Mengzhu Physical Review B, Vol. 102, Issue 16 https://doi.org/10.1103/PhysRevB.102.161115	journal	October 2020
All Magic Angles in Twisted Bilayer Graphene are Topological Song, Zhida; Wang, Zhijun; Shi, Wujun Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.036401	journal	July 2019
Quantum anomalous Hall effect with a permanent magnet defines a quantum resistance standard Okazaki, Yuma; Oe, Takehiko; Kawamura, Minoru Nature Physics, Vol. 18, Issue 1 https://doi.org/10.1038/s41567-021-01424-8	journal	December 2021
Emergence of superlattice Dirac points in graphene on hexagonal boron nitride Yankowitz, Matthew; Xue, Jiamin; Cormode, Daniel Nature Physics, Vol. 8, Issue 5 https://doi.org/10.1038/nphys2272	journal	March 2012
Double-slit photoelectron interference in strong-field ionization of the neon dimer Kunitski, Maksim; Eicke, Nicolas; Huber, Pia Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-018-07882-8	journal	January 2019
Evidence for magnetic Weyl fermions in a correlated metal Kuroda, K.; Tomita, T.; Suzuki, M. -T. Nature Materials, Vol. 16, Issue 11 https://doi.org/10.1038/nmat4987	journal	September 2017
Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene Lu, Xiaobo; Stepanov, Petr; Yang, Wei Nature, Vol. 574, Issue 7780 https://doi.org/10.1038/s41586-019-1695-0	journal	October 2019
Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026402	journal	July 2018
Mn‐Rich MnSb ₂ Te ₄ : A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45–50 K Wimmer, Stefan; Sánchez‐Barriga, Jaime; Küppers, Philipp Advanced Materials, Vol. 33, Issue 42 https://doi.org/10.1002/adma.202102935	journal	September 2021
Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator $MnB i_{2} T e_{4}$ Lee, Seng Huat; Zhu, Yanglin; Wang, Yu Physical Review Research, Vol. 1, Issue 1 https://doi.org/10.1103/PhysRevResearch.1.012011	journal	August 2019
Time Reversal Symmetric Topological Exciton Condensate in Bilayer HgTe Quantum Wells Budich, Jan Carl; Trauzettel, Björn; Michetti, Paolo Physical Review Letters, Vol. 112, Issue 14 https://doi.org/10.1103/PhysRevLett.112.146405	journal	April 2014
Metal-to-insulator switching in quantum anomalous Hall states Kou, Xufeng; Pan, Lei; Wang, Jing Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9474	journal	October 2015
A magnetic heterostructure of topological insulators as a candidate for an axion insulator Mogi, M.; Kawamura, M.; Yoshimi, R. Nature Materials, Vol. 16, Issue 5 https://doi.org/10.1038/nmat4855	journal	February 2017
Spontaneous strains and gap in graphene on boron nitride San-Jose, Pablo; Gutiérrez-Rubio, A.; Sturla, Mauricio Physical Review B, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevB.90.075428	journal	August 2014
Topological Axion States in the Magnetic Insulator ${MnBi}_{2} {Te}_{4}$ with the Quantized Magnetoelectric Effect Zhang, Dongqin; Shi, Minji; Zhu, Tongshuai Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.206401	journal	May 2019
On the new action of magnetism on a permanent electric current Hall, E. H. American Journal of Science, Vol. s3-20, Issue 117 https://doi.org/10.2475/ajs.s3-20.117.161	journal	September 1880
Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics Grauer, S.; Fijalkowski, K. M.; Schreyeck, S. Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.246801	journal	June 2017
Quantum oscillations in the field-induced ferromagnetic state of $Mn {Bi}_{2 - x} {Sb}_{x} {Te}_{4}$ Jiang, Qianni; Wang, Chong; Malinowski, Paul Physical Review B, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevB.103.205111	journal	May 2021
Valley-polarized quantum anomalous Hall phase in bilayer graphene with layer-dependent proximity effects Vila, Marc; Garcia, Jose H.; Roche, Stephan Physical Review B, Vol. 104, Issue 16 https://doi.org/10.1103/PhysRevB.104.L161113	journal	October 2021
Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect Mogi, M.; Yoshimi, R.; Tsukazaki, A. Applied Physics Letters, Vol. 107, Issue 18 https://doi.org/10.1063/1.4935075	journal	November 2015
Localization and scaling in the quantum Hall regime Wei, H. P.; Tsui, D. C.; Pruisken, A. M. M. Physical Review B, Vol. 33, Issue 2 https://doi.org/10.1103/PhysRevB.33.1488	journal	January 1986
Valley-Polarized Quantum Anomalous Hall Effect in Ferrimagnetic Honeycomb Lattices Zhou, Jian; Sun, Qiang; Jena, Puru Physical Review Letters, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRevLett.119.046403	journal	July 2017
Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures Xiao, Di; Zhu, Wenguang; Ran, Ying Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1602	journal	September 2011
The marvels of moiré materials Andrei, Eva Y.; Efetov, Dmitri K.; Jarillo-Herrero, Pablo Nature Reviews Materials, Vol. 6, Issue 3 https://doi.org/10.1038/s41578-021-00284-1	journal	March 2021
Unified model for two localization problems: Electron states in spin-degenerate Landau levels and in a random magnetic field Lee, D. K. K.; Chalker, J. T. Physical Review Letters, Vol. 72, Issue 10 https://doi.org/10.1103/PhysRevLett.72.1510	journal	March 1994
Topological Confinement in Bilayer Graphene Martin, Ivar; Blanter, Ya. M.; Morpurgo, A. F. Physical Review Letters, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevLett.100.036804	journal	January 2008
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 193, Issue 1 https://doi.org/10.1016/0550-3213(81)90524-1	journal	December 1981
Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures Rienks, E. D. L.; Wimmer, S.; Sánchez-Barriga, J. Nature, Vol. 576, Issue 7787 https://doi.org/10.1038/s41586-019-1826-7	journal	December 2019
Fractional Quantum Hall States at Zero Magnetic Field Neupert, Titus; Santos, Luiz; Chamon, Claudio Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236804	journal	June 2011
Experiments on Delocalization and University in the Integral Quantum Hall Effect Wei, H. P.; Tsui, D. C.; Paalanen, M. A. Physical Review Letters, Vol. 61, Issue 11 https://doi.org/10.1103/PhysRevLett.61.1294	journal	September 1988
High-Temperature Fractional Quantum Hall States Tang, Evelyn; Mei, Jia-Wei; Wen, Xiao-Gang Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236802	journal	June 2011
Magnetic Impurities on the Surface of a Topological Insulator Liu, Qin; Liu, Chao-Xing; Xu, Cenke Physical Review Letters, Vol. 102, Issue 15 https://doi.org/10.1103/PhysRevLett.102.156603	journal	April 2009
Nearly Flatbands with Nontrivial Topology Sun, Kai; Gu, Zhengcheng; Katsura, Hosho Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236803	journal	June 2011
Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film Jiang, Hua; Qiao, Zhenhua; Liu, Haiwen Physical Review B, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevB.85.045445	journal	January 2012
Itinerant Electron-Driven Chiral Magnetic Ordering and Spontaneous Quantum Hall Effect in Triangular Lattice Models Martin, Ivar; Batista, C. D. Physical Review Letters, Vol. 101, Issue 15 https://doi.org/10.1103/PhysRevLett.101.156402	journal	October 2008
Coexistence of Surface Ferromagnetism and a Gapless Topological State in ${MnBi}_{2} {Te}_{4}$ Nevola, D.; Li, H. X.; Yan, J. -Q. Physical Review Letters, Vol. 125, Issue 11 https://doi.org/10.1103/PhysRevLett.125.117205	journal	September 2020
Correlation-driven topological phases in magic-angle twisted bilayer graphene Choi, Youngjoon; Kim, Hyunjin; Peng, Yang Nature, Vol. 589, Issue 7843 https://doi.org/10.1038/s41586-020-03159-7	journal	January 2021
Prediction of a quantum anomalous Hall state in Co-decorated silicene Kaloni, T. P.; Singh, N.; Schwingenschlögl, U. Physical Review B, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevB.89.035409	journal	January 2014
High-Chern-number and high-temperature quantum Hall effect without Landau levels Ge, Jun; Liu, Yanzhao; Li, Jiaheng National Science Review, Vol. 7, Issue 8 https://doi.org/10.1093/nsr/nwaa089	journal	April 2020
A-type antiferromagnetic order in ${MnBi}_{4} {Te}_{7}$ and ${MnBi}_{6} {Te}_{10}$ single crystals Yan, J. -Q.; Liu, Y. H.; Parker, D. S. Physical Review Materials, Vol. 4, Issue 5 https://doi.org/10.1103/PhysRevMaterials.4.054202	journal	May 2020
Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators Zhao, Yi-Fan; Zhang, Ruoxi; Zhou, Ling-Jie Physical Review Letters, Vol. 128, Issue 21 https://doi.org/10.1103/PhysRevLett.128.216801	journal	May 2022
Atomically smooth ultrathin films of topological insulator Sb2Te3 Wang, Guang; Zhu, Xiegang; Wen, Jing Nano Research, Vol. 3, Issue 12 https://doi.org/10.1007/s12274-010-0060-2	journal	November 2010
Breakdown of the integer quantum Hall effect at high currents in GaAs/AlGaAs heterostructures Kawaji, S. Semiconductor Science and Technology, Vol. 11, Issue 11S https://doi.org/10.1088/0268-1242/11/11S/016	journal	November 1996
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface Xia, Y.; Qian, D.; Hsieh, D. Nature Physics, Vol. 5, Issue 6, p. 398-402 https://doi.org/10.1038/nphys1274	journal	May 2009
Spin valleytronics in silicene: Quantum spin Hall–quantum anomalous Hall insulators and single-valley semimetals Ezawa, Motohiko Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155415	journal	April 2013
Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene Liu, Jianpeng; Dai, Xi Physical Review B, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevB.103.035427	journal	January 2021
Robust $A$ -Type Order and Spin-Flop Transition on the Surface of the Antiferromagnetic Topological Insulator ${MnBi}_{2} {Te}_{4}$ Sass, Paul M.; Kim, Jinwoong; Vanderbilt, David Physical Review Letters, Vol. 125, Issue 3 https://doi.org/10.1103/PhysRevLett.125.037201	journal	July 2020
Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang Nature Physics, Vol. 5, Issue 6, p. 438-442 https://doi.org/10.1038/nphys1270	journal	May 2009
Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators Essin, Andrew M.; Moore, Joel E.; Vanderbilt, David Physical Review Letters, Vol. 102, Issue 14 https://doi.org/10.1103/PhysRevLett.102.146805	journal	April 2009
Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator Liu, Chang; Wang, Yongchao; Li, Hao Nature Materials https://doi.org/10.1038/s41563-019-0573-3	journal	January 2020
Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei Physical Review Letters, Vol. 112, Issue 4 https://doi.org/10.1103/PhysRevLett.112.046801	journal	January 2014
The fractional quantum Hall effect Stormer, Horst L.; Tsui, Daniel C.; Gossard, Arthur C. Reviews of Modern Physics, Vol. 71, Issue 2 https://doi.org/10.1103/RevModPhys.71.S298	journal	March 1999
Quantum Spin Hall and Quantum Anomalous Hall States Realized in Junction Quantum Wells Zhang, Haijun; Xu, Yong; Wang, Jing Physical Review Letters, Vol. 112, Issue 21 https://doi.org/10.1103/PhysRevLett.112.216803	journal	May 2014
Quantum anomalous Hall effect in stanene on a nonmagnetic substrate Zhang, Huisheng; Zhou, Tong; Zhang, Jiayong Physical Review B, Vol. 94, Issue 23 https://doi.org/10.1103/PhysRevB.94.235409	journal	December 2016
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene Ezawa, Motohiko Physical Review Letters, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRevLett.109.055502	journal	August 2012
Tailoring tricolor structure of magnetic topological insulator for robust axion insulator Mogi, Masataka; Kawamura, Minoru; Tsukazaki, Atsushi Science Advances, Vol. 3, Issue 10 https://doi.org/10.1126/sciadv.aao1669	journal	October 2017
Strongly correlated Chern insulators in magic-angle twisted bilayer graphene Nuckolls, Kevin P.; Oh, Myungchul; Wong, Dillon Nature, Vol. 588, Issue 7839 https://doi.org/10.1038/s41586-020-3028-8	journal	December 2020
Crystal and magnetic structures of magnetic topological insulators ${MnBi}_{2} {Te}_{4}$ and ${MnBi}_{4} {Te}_{7}$ Ding, Lei; Hu, Chaowei; Ye, Feng Physical Review B, Vol. 101, Issue 2 https://doi.org/10.1103/PhysRevB.101.020412	journal	January 2020
Quantum Anomalous Parity Hall Effect in Magnetically Disordered Topological Insulator Films Haim, Arbel; Ilan, Roni; Alicea, Jason Physical Review Letters, Vol. 123, Issue 4 https://doi.org/10.1103/PhysRevLett.123.046801	journal	July 2019
Controllable quantum point junction on the surface of an antiferromagnetic topological insulator Varnava, Nicodemos; Wilson, Justin H.; Pixley, J. H. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-24276-5	journal	June 2021
Development of ferromagnetism in the doped topological insulator ${Bi}_{2 - x} {Mn}_{x} {Te}_{3}$ Hor, Y. S.; Roushan, P.; Beidenkopf, H. Physical Review B, Vol. 81, Issue 19 https://doi.org/10.1103/PhysRevB.81.195203	journal	May 2010
Topological invariants of time-reversal-invariant band structures Moore, J. E.; Balents, L. Physical Review B, Vol. 75, Issue 12, Article No. 121306(R) https://doi.org/10.1103/PhysRevB.75.121306	journal	March 2007
Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene Wu, Shuang; Zhang, Zhenyuan; Watanabe, K. Nature Materials, Vol. 20, Issue 4 https://doi.org/10.1038/s41563-020-00911-2	journal	February 2021
Marriage of topology and magnetism Chang, Cui-Zu Nature Materials, Vol. 19, Issue 5 https://doi.org/10.1038/s41563-020-0632-9	journal	March 2020
Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions Das, Anindya; Ronen, Yuval; Most, Yonatan Nature Physics, Vol. 8, Issue 12 https://doi.org/10.1038/nphys2479	journal	November 2012
Rashba effect at magnetic metal surfaces Krupin, O.; Bihlmayer, G.; Starke, K. Physical Review B, Vol. 71, Issue 20 https://doi.org/10.1103/PhysRevB.71.201403	journal	May 2005
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance Klitzing, K. v.; Dorda, G.; Pepper, M. Physical Review Letters, Vol. 45, Issue 6 https://doi.org/10.1103/PhysRevLett.45.494	journal	August 1980
Chiral transport along magnetic domain walls in the quantum anomalous Hall effect Rosen, Ilan T.; Fox, Eli J.; Kou, Xufeng npj Quantum Materials, Vol. 2, Issue 1 https://doi.org/10.1038/s41535-017-0073-0	journal	December 2017
Graphene Bilayer with a Twist: Electronic Structure Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H. Physical Review Letters, Vol. 99, Issue 25 https://doi.org/10.1103/PhysRevLett.99.256802	journal	December 2007
Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures Huang, Yingyi; Setiawan, F.; Sau, Jay D. Physical Review B, Vol. 97, Issue 10 https://doi.org/10.1103/PhysRevB.97.100501	journal	March 2018
The Quantum Anomalous Hall Effect: Theory and Experiment Liu, Chao-Xing; Zhang, Shou-Cheng; Qi, Xiao-Liang Annual Review of Condensed Matter Physics, Vol. 7, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031115-011417	journal	March 2016
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
Effects of Random Domains on the Zero Hall Plateau in the Quantum Anomalous Hall Effect Chen, Chui-Zhen; Liu, Haiwen; Xie, X. C. Physical Review Letters, Vol. 122, Issue 2 https://doi.org/10.1103/PhysRevLett.122.026601	journal	January 2019
Investigating and manipulating the molecular beam epitaxy growth kinetics of intrinsic magnetic topological insulator MnBi ₂ Te ₄ with in situ angle-resolved photoemission spectroscopy Zhu, Kejing; Bai, Yunhe; Hong, Xiyu Journal of Physics: Condensed Matter, Vol. 32, Issue 47 https://doi.org/10.1088/1361-648X/aba06d	journal	September 2020
Integer and fractional quantum anomalous Hall effect in a strip of stripes model Klinovaja, Jelena; Tserkovnyak, Yaroslav; Loss, Daniel Physical Review B, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevB.91.085426	journal	February 2015
Fractional Chern insulator states in twisted bilayer graphene: An analytical approach Ledwith, Patrick J.; Tarnopolsky, Grigory; Khalaf, Eslam Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023237	journal	May 2020
Electric control of a canted-antiferromagnetic Chern insulator Cai, Jiaqi; Ovchinnikov, Dmitry; Fei, Zaiyao Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-29259-8	journal	March 2022
Chern bands of twisted bilayer graphene: Fractional Chern insulators and spin phase transition Repellin, Cécile; Senthil, T. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023238	journal	May 2020
Quantum anomalous Hall effect from intertwined moiré bands Li, Tingxin; Jiang, Shengwei; Shen, Bowen Nature, Vol. 600, Issue 7890 https://doi.org/10.1038/s41586-021-04171-1	journal	December 2021
Persistent surface states with diminishing gap in MnBi2Te4/Bi2Te3 superlattice antiferromagnetic topological insulator Xu, Lixuan; Mao, Yuanhao; Wang, Hongyuan Science Bulletin, Vol. 65, Issue 24 https://doi.org/10.1016/j.scib.2020.07.032	journal	December 2020
Quantum anomalous Hall effect in single-layer and bilayer graphene Tse, Wang-Kong; Qiao, Zhenhua; Yao, Yugui Physical Review B, Vol. 83, Issue 15 https://doi.org/10.1103/PhysRevB.83.155447	journal	April 2011
Using nonlocal surface transport to identify the axion insulator Chen, Rui; Li, Shuai; Sun, Hai-Peng Physical Review B, Vol. 103, Issue 24 https://doi.org/10.1103/PhysRevB.103.L241409	journal	June 2021
Berry Phase Correction to Electron Density of States in Solids Xiao, Di; Shi, Junren; Niu, Qian Physical Review Letters, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevLett.95.137204	journal	September 2005
Orbital Magnetization in Periodic Insulators Thonhauser, T.; Ceresoli, Davide; Vanderbilt, David Physical Review Letters, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevLett.95.137205	journal	September 2005
Superconductivity and strong correlations in moiré flat bands Balents, Leon; Dean, Cory R.; Efetov, Dmitri K. Nature Physics, Vol. 16, Issue 7 https://doi.org/10.1038/s41567-020-0906-9	journal	May 2020
Magnetic and transport properties in the magnetic topological insulators MnB i 2 T e 4 ( B i 2 T e 3 ) n ( n = 1 , 2 ) Shi, M. Z.; Lei, B.; Zhu, C. S. Physical Review B, Vol. 100, Issue 15 https://doi.org/10.1103/PhysRevB.100.155144	journal	October 2019
Topological field theory of time-reversal invariant insulators Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 78, Issue 19, Article No. 195424 https://doi.org/10.1103/PhysRevB.78.195424	journal	November 2008
Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit Zhang, Yi; He, Ke; Chang, Cui-Zu Nature Physics, Vol. 6, Issue 8 https://doi.org/10.1038/nphys1689	journal	June 2010
$\frac{1}{2} (e^{2} / h)$ Conductance Plateau without 1D Chiral Majorana Fermions Ji, Wenjie; Wen, Xiao-Gang Physical Review Letters, Vol. 120, Issue 10 https://doi.org/10.1103/PhysRevLett.120.107002	journal	March 2018
$CP$ Conservation in the Presence of Pseudoparticles Peccei, R. D.; Quinn, Helen R. Physical Review Letters, Vol. 38, Issue 25 https://doi.org/10.1103/PhysRevLett.38.1440	journal	June 1977
Adsorption-controlled growth of $MnTe {({Bi}_{2} {Te}_{3})}_{n}$ by molecular beam epitaxy exhibiting stoichiometry-controlled magnetism Lapano, Jason; Nuckols, Lauren; Mazza, Alessandro R. Physical Review Materials, Vol. 4, Issue 11 https://doi.org/10.1103/PhysRevMaterials.4.111201	journal	November 2020
Electrically tunable spin polarization of chiral edge modes in a quantum anomalous Hall insulator Zhang, Rui-Xing; Hsu, Hsiu-Chuan; Liu, Chao-Xing Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235315	journal	June 2016
Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices Kayyalha, Morteza; Xiao, Di; Zhang, Ruoxi Science, Vol. 367, Issue 6473 https://doi.org/10.1126/science.aax6361	journal	January 2020
Magnetic topological insulator ${MnBi}_{6} {Te}_{10}$ with a zero-field ferromagnetic state and gapped Dirac surface states Tian, Shangjie; Gao, Shunye; Nie, Simin Physical Review B, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevB.102.035144	journal	July 2020
Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator Kandala, Abhinav; Richardella, Anthony; Kempinger, Susan Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8434	journal	July 2015
Multiple Weyl fermions and tunable quantum anomalous Hall effect in 2D half-metal with huge spin-related energy gap Meng, Weizhen; Zhang, Xiaoming; Yu, Weiwang Applied Surface Science, Vol. 551 https://doi.org/10.1016/j.apsusc.2021.149390	journal	June 2021
Magnetic topological insulators Tokura, Yoshinori; Yasuda, Kenji; Tsukazaki, Atsushi Nature Reviews Physics, Vol. 1, Issue 2 https://doi.org/10.1038/s42254-018-0011-5	journal	January 2019
Native defects in antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$ Huang, Zengle; Du, Mao-Hua; Yan, Jiaqiang Physical Review Materials, Vol. 4, Issue 12 https://doi.org/10.1103/PhysRevMaterials.4.121202	journal	December 2020
Superexchange dominates in magnetic topological insulators Śliwa, Cezary; Autieri, Carmine; Majewski, Jacek A. Physical Review B, Vol. 104, Issue 22 https://doi.org/10.1103/PhysRevB.104.L220404	journal	December 2021
Quantum Anomalous Hall Effect in ${Hg}_{1 - y} {Mn}_{y} Te$ Quantum Wells Liu, Chao-Xing; Qi, Xiao-Liang; Dai, Xi Physical Review Letters, Vol. 101, Issue 14 https://doi.org/10.1103/PhysRevLett.101.146802	journal	October 2008
Robust quantum anomalous Hall effect with electrically tunable band gap in Ta-decorated silicene Qian, Jiahui; Zhang, Jiayong; Wu, Qixing Applied Physics Letters, Vol. 114, Issue 5 https://doi.org/10.1063/1.5065789	journal	February 2019
Surfaces of axion insulators Varnava, Nicodemos; Vanderbilt, David Physical Review B, Vol. 98, Issue 24 https://doi.org/10.1103/PhysRevB.98.245117	journal	December 2018
Faithful tight-binding models and fragile topology of magic-angle bilayer graphene Po, Hoi Chun; Zou, Liujun; Senthil, T. Physical Review B, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevB.99.195455	journal	May 2019
Current-Driven Instability of the Quantum Anomalous Hall Effect in Ferromagnetic Topological Insulators Kawamura, Minoru; Yoshimi, Ryutaro; Tsukazaki, Atsushi Physical Review Letters, Vol. 119, Issue 1 https://doi.org/10.1103/PhysRevLett.119.016803	journal	July 2017
Mass acquisition of Dirac fermions in magnetically doped topological insulator $S b_{2} T e_{3}$ films Jiang, Yeping; Song, Canli; Li, Zhi Physical Review B, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevB.92.195418	journal	November 2015
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. Proceedings of the National Academy of Sciences, Vol. 108, Issue 30 https://doi.org/10.1073/pnas.1108174108	journal	July 2011
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Demir, Ahmet Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26154	journal	March 2018
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Hybridization-induced gapped and gapless states on the surface of magnetic topological insulators Ma, Xiao-Ming; Chen, Zhongjia; Schwier, Eike F. Physical Review B, Vol. 102, Issue 24 https://doi.org/10.1103/PhysRevB.102.245136	journal	December 2020
The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles Rokhinson, Leonid P.; Liu, Xinyu; Furdyna, Jacek K. Nature Physics, Vol. 8, Issue 11 https://doi.org/10.1038/nphys2429	journal	September 2012
Gate-tunable quantum anomalous Hall effects in ${MnBi}_{2} {Te}_{4}$ thin films Lei, Chao; MacDonald, A. H. Physical Review Materials, Vol. 5, Issue 5 https://doi.org/10.1103/PhysRevMaterials.5.L051201	journal	May 2021
Origin of the low critical observing temperature of the quantum anomalous Hall effect in V-doped (Bi, Sb)2Te3 film Li, W.; Claassen, M.; Chang, Cui-Zu Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep32732	journal	September 2016
Interaction between the $d$ -Shells in the Transition Metals. II. Ferromagnetic Compounds of Manganese with Perovskite Structure Zener, Clarence Physical Review, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRev.82.403	journal	May 1951
Orbital magnetic states in moiré graphene systems Liu, Jianpeng; Dai, Xi Nature Reviews Physics, Vol. 3, Issue 5 https://doi.org/10.1038/s42254-021-00297-3	journal	April 2021
Observation of Van Hove singularities in twisted graphene layers Li, Guohong; Luican, A.; Lopes dos Santos, J. M. B. Nature Physics, Vol. 6, Issue 2 https://doi.org/10.1038/nphys1463	journal	November 2009
Dilute ferromagnetic semiconductors: Physics and spintronic structures Dietl, Tomasz; Ohno, Hideo Reviews of Modern Physics, Vol. 86, Issue 1 https://doi.org/10.1103/RevModPhys.86.187	journal	March 2014
Quantum Anomalous Hall Multilayers Grown by Molecular Beam Epitaxy Jiang, Gaoyuan; Feng, Yang; Wu, Weixiong Chinese Physics Letters, Vol. 35, Issue 7 https://doi.org/10.1088/0256-307X/35/7/076802	journal	June 2018
U1 snRNP regulates cancer cell migration and invasion in vitro Oh, Jung-Min; Venters, Christopher C.; Di, Chao Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-019-13993-7	journal	January 2020
Above 400-K robust perpendicular ferromagnetic phase in a topological insulator Tang, Chi; Chang, Cui-Zu; Zhao, Gejian Science Advances, Vol. 3, Issue 6 https://doi.org/10.1126/sciadv.1700307	journal	June 2017
Condensed-Matter Simulation of a Three-Dimensional Anomaly Semenoff, Gordon W. Physical Review Letters, Vol. 53, Issue 26 https://doi.org/10.1103/PhysRevLett.53.2449	journal	December 1984
Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi ₂ Te ₄ Ovchinnikov, Dmitry; Huang, Xiong; Lin, Zhong Nano Letters, Vol. 21, Issue 6 https://doi.org/10.1021/acs.nanolett.0c05117	journal	March 2021
Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase Liu, Jianpeng; Liu, Junwei; Dai, Xi Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155415	journal	April 2019
Quasi-one-dimensional quantum anomalous Hall systems as new platforms for scalable topological quantum computation Chen, Chui-Zhen; Xie, Ying-Ming; Liu, Jie Physical Review B, Vol. 97, Issue 10 https://doi.org/10.1103/PhysRevB.97.104504	journal	March 2018
Experimental Verification of the Van Vleck Nature of Long-Range Ferromagnetic Order in the Vanadium-Doped Three-Dimensional Topological Insulator ${Sb}_{2} {Te}_{3}$ Li, Mingda; Chang, Cui-Zu; Wu, Lijun Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.146802	journal	April 2015
Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure He, Qing Lin; Pan, Lei; Stern, Alexander L. Science, Vol. 357, Issue 6348 https://doi.org/10.1126/science.aag2792	journal	July 2017
Nonequilibrium breakdown of quantum Hall state in graphene Singh, Vibhor; Deshmukh, Mandar M. Physical Review B, Vol. 80, Issue 8 https://doi.org/10.1103/PhysRevB.80.081404	journal	August 2009
Impurity states in the magnetic topological insulator $V : {(Bi, Sb)}_{2} {Te}_{3}$ Peixoto, Thiago R. F.; Bentmann, Hendrik; Schreyeck, Steffen Physical Review B, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevB.94.195140	journal	November 2016
Electrically-driven Domain Wall Motion in Quantum Anomalous Hall States Kim, Sehoon; Kurebayashi, Daichi; Nomura, Kentaro Journal of the Physical Society of Japan, Vol. 88, Issue 8 https://doi.org/10.7566/JPSJ.88.083704	journal	August 2019
Realization of an intrinsic ferromagnetic topological state in MnBi ₈ Te ₁₃ Hu, Chaowei; Ding, Lei; Gordon, Kyle N. Science Advances, Vol. 6, Issue 30 https://doi.org/10.1126/sciadv.aba4275	journal	July 2020
Properties of ferromagnetic III–V semiconductors Ohno, Hideo Journal of Magnetism and Magnetic Materials, Vol. 200, Issue 1-3 https://doi.org/10.1016/S0304-8853(99)00444-8	journal	October 1999
Thin-film ferromagnetic semiconductors based on Sb2−xVxTe3 with TC of 177K Zhou, Zhenhua; Chien, Yi-Jiunn; Uher, Ctirad Applied Physics Letters, Vol. 87, Issue 11 https://doi.org/10.1063/1.2045561	journal	September 2005
Field-effect modulation of anomalous Hall effect in diluted ferromagnetic topological insulator epitaxial films Chang, CuiZu; Liu, MinHao; Zhang, ZuoCheng Science China Physics, Mechanics & Astronomy, Vol. 59, Issue 3 https://doi.org/10.1007/s11433-015-5761-9	journal	January 2016
Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals Onoda, Masaru; Nagaosa, Naoto Physical Review Letters, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevLett.90.206601	journal	May 2003
Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene Bultinck, Nick; Chatterjee, Shubhayu; Zaletel, Michael P. Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/PhysRevLett.124.166601	journal	April 2020
Effects of domain walls in quantum anomalous Hall insulator/superconductor heterostructures Chen, Chui-Zhen; He, James Jun; Xu, Dong-Hui Physical Review B, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevB.96.041118	journal	July 2017
Valley-Polarized Quantum Anomalous Hall Effect in Silicene Pan, Hui; Li, Zhenshan; Liu, Cheng-Cheng Physical Review Letters, Vol. 112, Issue 10 https://doi.org/10.1103/PhysRevLett.112.106802	journal	March 2014
Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator Chen, Y. L.; Chu, J. - H.; Analytis, J. G. Science, Vol. 329, Issue 5992 https://doi.org/10.1126/science.1189924	journal	August 2010
High-current breakdown of the quantum Hall effect and electron heating in InSb/AlInSb Alexander-Webber, J. A.; Baker, A. M. R.; Buckle, P. D. Physical Review B, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevB.86.045404	journal	July 2012
Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals Ceresoli, Davide; Thonhauser, T.; Vanderbilt, David Physical Review B, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevB.74.024408	journal	July 2006
Topological Phases in AB-Stacked MoTe2/WSe2 : Z2 Topological Insulators, Chern Insulators, and Topological Charge Density Waves Pan, Haining; Xie, Ming; Wu, Fengcheng Physical Review Letters, Vol. 129, Issue 5 https://doi.org/10.1103/PhysRevLett.129.056804	journal	July 2022
Testing universality of the quantum Hall effect by means of the Wheatstone bridge Schopfer, F.; Poirier, W. Journal of Applied Physics, Vol. 102, Issue 5 https://doi.org/10.1063/1.2776371	journal	September 2007
Evolution of structural, magnetic, and transport properties in ${MnBi}_{2 - x} {Sb}_{x} {Te}_{4}$ Yan, J. -Q.; Okamoto, S.; McGuire, M. A. Physical Review B, Vol. 100, Issue 10 https://doi.org/10.1103/PhysRevB.100.104409	journal	September 2019
Layer Hall effect in a 2D topological axion antiferromagnet Gao, Anyuan; Liu, Yu-Fei; Hu, Chaowei Nature, Vol. 595, Issue 7868 https://doi.org/10.1038/s41586-021-03679-w	journal	July 2021
Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice Chen, Guorui; Sharpe, Aaron L.; Fox, Eli J. Nature, Vol. 579, Issue 7797 https://doi.org/10.1038/s41586-020-2049-7	journal	March 2020
Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices Mourik, V.; Zuo, K.; Frolov, S. M. Science, Vol. 336, Issue 6084 https://doi.org/10.1126/science.1222360	journal	April 2012
Chromium-induced ferromagnetism with perpendicular anisotropy in topological crystalline insulator SnTe (111) thin films Wang, Fei; Zhang, Hongrui; Jiang, Jue Physical Review B, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevB.97.115414	journal	March 2018
Search for Majorana Fermions in Superconductors Beenakker, C. W. J. Annual Review of Condensed Matter Physics, Vol. 4, Issue 1 https://doi.org/10.1146/annurev-conmatphys-030212-184337	journal	April 2013
Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing Bernevig, B. Andrei; Lian, Biao; Cowsik, Aditya Physical Review B, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevB.103.205415	journal	May 2021
Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram Lian, Biao; Song, Zhi-Da; Regnault, Nicolas Physical Review B, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevB.103.205414	journal	May 2021
Realization of interlayer ferromagnetic interaction in $MnS b_{2} T e_{4}$ toward the magnetic Weyl semimetal state Murakami, Taito; Nambu, Yusuke; Koretsune, Takashi Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevB.100.195103	journal	November 2019
Twisted bilayer graphene. II. Stable symmetry anomaly Song, Zhi-Da; Lian, Biao; Regnault, Nicolas Physical Review B, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevB.103.205412	journal	May 2021
Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior Chang, Cui-Zu; Zhao, Weiwei; Li, Jian Physical Review Letters, Vol. 117, Issue 12 https://doi.org/10.1103/PhysRevLett.117.126802	journal	September 2016
Two applications of axion electrodynamics Wilczek, Frank Physical Review Letters, Vol. 58, Issue 18 https://doi.org/10.1103/PhysRevLett.58.1799	journal	May 1987
Ordering mechanism and quantum anomalous Hall effect of magnetically doped topological insulators Kim, Jeongwoo; Jhi, Seung-Hoon; MacDonald, A. H. Physical Review B, Vol. 96, Issue 14 https://doi.org/10.1103/PhysRevB.96.140410	journal	October 2017
Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor Nadj-Perge, S.; Drozdov, I. K.; Li, J. Science, Vol. 346, Issue 6209 https://doi.org/10.1126/science.1259327	journal	October 2014
New classes of topological crystalline insulators having surface rotation anomaly Fang, Chen; Fu, Liang Science Advances, Vol. 5, Issue 12 https://doi.org/10.1126/sciadv.aat2374	journal	December 2019
Precise Quantization of the Anomalous Hall Effect near Zero Magnetic Field Bestwick, A. J.; Fox, E. J.; Kou, Xufeng Physical Review Letters, Vol. 114, Issue 18 https://doi.org/10.1103/PhysRevLett.114.187201	journal	May 2015
Twistable electronics with dynamically rotatable heterostructures Ribeiro-Palau, Rebeca; Zhang, Changjian; Watanabe, Kenji Science, Vol. 361, Issue 6403 https://doi.org/10.1126/science.aat6981	journal	August 2018
Quantum Anomalous Hall Effect from Inverted Charge Transfer Gap Devakul, Trithep; Fu, Liang Physical Review X, Vol. 12, Issue 2 https://doi.org/10.1103/PhysRevX.12.021031	journal	May 2022
Stanene on a SiC(0001) surface: a candidate for realizing quantum anomalous Hall effect Li, Ping Physical Chemistry Chemical Physics, Vol. 21, Issue 21 https://doi.org/10.1039/C9CP01509D	journal	January 2019
Quantum phase transition of chiral Majorana fermions in the presence of disorder Lian, Biao; Wang, Jing; Sun, Xiao-Qi Physical Review B, Vol. 97, Issue 12 https://doi.org/10.1103/PhysRevB.97.125408	journal	March 2018
A Theory of Metallic Ferro- and Antiferromagnetism on Zener's Model Kasuya, Tadao Progress of Theoretical Physics, Vol. 16, Issue 1 https://doi.org/10.1143/PTP.16.45	journal	July 1956
Continuous Mott transition in semiconductor moiré superlattices Li, Tingxin; Jiang, Shengwei; Li, Lizhong Nature, Vol. 597, Issue 7876 https://doi.org/10.1038/s41586-021-03853-0	journal	September 2021
Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene Kim, Kyounghwan; DaSilva, Ashley; Huang, Shengqiang Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1620140114	journal	March 2017
Ultrastructural Characterization of the Lower Motor System in a Mouse Model of Krabbe Disease Cappello, Valentina; Marchetti, Laura; Parlanti, Paola Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/s41598-016-0001-8	journal	December 2016
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Science, Vol. 314, Issue 5806, p. 1757-1761 https://doi.org/10.1126/science.1133734	journal	December 2006
Chemical-Potential-Dependent Gap Opening at the Dirac Surface States of ${Bi}_{2} {Se}_{3}$ Induced by Aggregated Substitutional Cr Atoms Chang, Cui-Zu; Tang, Peizhe; Wang, Yi-Lin Physical Review Letters, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRevLett.112.056801	journal	February 2014
New directions in the pursuit of Majorana fermions in solid state systems Alicea, Jason Reports on Progress in Physics, Vol. 75, Issue 7 https://doi.org/10.1088/0034-4885/75/7/076501	journal	June 2012
Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems Qiao, Zhenhua; Han, Yulei; Zhang, Lei Physical Review Letters, Vol. 117, Issue 5 https://doi.org/10.1103/PhysRevLett.117.056802	journal	July 2016
Converting a two-dimensional ferromagnetic insulator into a high-temperature quantum anomalous Hall system by means of an appropriate surface modification Zhang, Huisheng; Qin, Wei; Chen, Mingxing Physical Review B, Vol. 99, Issue 16 https://doi.org/10.1103/PhysRevB.99.165410	journal	April 2019
Quantum anomalous Hall effect and related topological electronic states Weng, Hongming; Yu, Rui; Hu, Xiao Advances in Physics, Vol. 64, Issue 3 https://doi.org/10.1080/00018732.2015.1068524	journal	May 2015
Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport Xiao, Di; Yao, Wang; Niu, Qian Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236809	journal	December 2007
Superexchange interaction and symmetry properties of electron orbitals Kanamori, Junjiro Journal of Physics and Chemistry of Solids, Vol. 10, Issue 2-3 https://doi.org/10.1016/0022-3697(59)90061-7	journal	July 1959
Topological phases and the quantum spin Hall effect in three dimensions Roy, Rahul Physical Review B, Vol. 79, Issue 19 https://doi.org/10.1103/PhysRevB.79.195322	journal	May 2009
Diamagnetismus der Metalle Landau, L. Zeitschrift f�r Physik, Vol. 64, Issue 9-10 https://doi.org/10.1007/BF01397213	journal	September 1930
Realizing both giant magnetic anisotropy and quantum anomalous Hall effect in graphene with adsorbed Te-Co dimer Zhang, Kai-Cheng; Li, Yong-Feng; Liu, Yong Journal of Physics: Condensed Matter, Vol. 31, Issue 4 https://doi.org/10.1088/1361-648X/aaf212	journal	December 2018
Spin Fluctuations in Quantized Transport of Magnetic Topological Insulators Li, Yu-Hang; Cheng, Ran Physical Review Letters, Vol. 126, Issue 2 https://doi.org/10.1103/PhysRevLett.126.026601	journal	January 2021
Direct evidence of ferromagnetism in a quantum anomalous Hall system Wang, Wenbo; Ou, Yunbo; Liu, Chang Nature Physics, Vol. 14, Issue 8 https://doi.org/10.1038/s41567-018-0149-1	journal	May 2018
Intrinsic magnetic topological insulators in van der Waals layered MnBi ₂ Te ₄ -family materials Li, Jiaheng; Li, Yang; Du, Shiqiao Science Advances, Vol. 5, Issue 6 https://doi.org/10.1126/sciadv.aaw5685	journal	June 2019
Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers Zhang, Yang; Devakul, Trithep; Fu, Liang Proceedings of the National Academy of Sciences, Vol. 118, Issue 36 https://doi.org/10.1073/pnas.2112673118	journal	September 2021
Zero-Field Dissipationless Chiral Edge Transport and the Nature of Dissipation in the Quantum Anomalous Hall State Chang, Cui-Zu; Zhao, Weiwei; Kim, Duk Y. Physical Review Letters, Vol. 115, Issue 5 https://doi.org/10.1103/PhysRevLett.115.057206	journal	July 2015
Voltage-Controlled Magnetic Reversal in Orbital Chern Insulators Zhu, Jihang; Su, Jung-Jung; MacDonald, A. H. Physical Review Letters, Vol. 125, Issue 22 https://doi.org/10.1103/PhysRevLett.125.227702	journal	November 2020
Topology-Driven Magnetic Quantum Phase Transition in Topological Insulators Zhang, J.; Chang, C. -Z.; Tang, P. Science, Vol. 339, Issue 6127 https://doi.org/10.1126/science.1230905	journal	March 2013
Abundant topological states in silicene with transition metal adatoms Zhang, Jiayong; Zhao, Bao; Yang, Zhongqin Physical Review B, Vol. 88, Issue 16 https://doi.org/10.1103/PhysRevB.88.165422	journal	October 2013
Landau-level subband structure of electrons on a square lattice MacDonald, A. H. Physical Review B, Vol. 28, Issue 12 https://doi.org/10.1103/PhysRevB.28.6713	journal	December 1983
Current scaling of the topological quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator Kawamura, Minoru; Mogi, Masataka; Yoshimi, Ryutaro Physical Review B, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevB.102.041301	journal	July 2020
Anomalous Zero-Bias Conductance Peak in a Nb–InSb Nanowire–Nb Hybrid Device Deng, M. T.; Yu, C. L.; Huang, G. Y. Nano Letters, Vol. 12, Issue 12 https://doi.org/10.1021/nl303758w	journal	February 2012
Any axion insulator must be a bulk three-dimensional topological insulator Fijalkowski, K. M.; Liu, N.; Hartl, M. Physical Review B, Vol. 103, Issue 23 https://doi.org/10.1103/PhysRevB.103.235111	journal	June 2021
Thickness Dependence of the Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films Feng, Xiao; Feng, Yang; Wang, Jing Advanced Materials, Vol. 28, Issue 30 https://doi.org/10.1002/adma.201600919	journal	May 2016
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Microscopic theory of quantum anomalous Hall effect in graphene Qiao, Zhenhua; Jiang, Hua; Li, Xiao Physical Review B, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevB.85.115439	journal	March 2012
Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi ₂ Te ₄ Deng, Yujun; Yu, Yijun; Shi, Meng Zhu Science, Vol. 367, Issue 6480 https://doi.org/10.1126/science.aax8156	journal	January 2020
Intrinsic Topological Insulator Bi2Te3 Thin Films on Si and Their Thickness Limit Li, Yao-Yi; Wang, Guang; Zhu, Xie-Gang Advanced Materials, Vol. 22, Issue 36 https://doi.org/10.1002/adma.201000368	journal	July 2010
Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃ Lee, Inhee; Kim, Chung Koo; Lee, Jinho Proceedings of the National Academy of Sciences, Vol. 112, Issue 5 https://doi.org/10.1073/pnas.1424322112	journal	January 2015
Topological magnetoelectric effects in thin films of topological insulators Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.085113	journal	August 2015
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aav1910	journal	January 2019
Natural van der Waals heterostructural single crystals with both magnetic and topological properties Wu, Jiazhen; Liu, Fucai; Sasase, Masato Science Advances, Vol. 5, Issue 11 https://doi.org/10.1126/sciadv.aax9989	journal	November 2019
Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry Ahn, Junyeong; Yang, Bohm-Jung Physical Review Letters, Vol. 118, Issue 15 https://doi.org/10.1103/PhysRevLett.118.156401	journal	April 2017
High-current effects in magnetotransport of two-dimensional electrons in GaAs/AlxGa1−xAs heterostructures Mensz, P. M.; Tsui, D. C. Physical Review B, Vol. 40, Issue 6 https://doi.org/10.1103/PhysRevB.40.3919	journal	August 1989
Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators Chang, Cui-Zu; Li, Mingda Journal of Physics: Condensed Matter, Vol. 28, Issue 12 https://doi.org/10.1088/0953-8984/28/12/123002	journal	March 2016
Molecular beam epitaxy of antiferromagnetic (MnBi ₂ Te ₄ )(Bi ₂ Te ₃ ) thin films on BaF ₂ (111) Kagerer, P.; Fornari, C. I.; Buchberger, S. Journal of Applied Physics, Vol. 128, Issue 13 https://doi.org/10.1063/5.0025933	journal	October 2020
Giant gap quantum spin Hall effect and valley-polarized quantum anomalous Hall effect in cyanided bismuth bilayers Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng New Journal of Physics, Vol. 18, Issue 8 https://doi.org/10.1088/1367-2630/18/8/083002	journal	July 2016
Quantum anomalous Hall effect in ferromagnetic transition metal halides Huang, Chengxi; Zhou, Jian; Wu, Haiping Physical Review B, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevB.95.045113	journal	January 2017
Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state Okada, Ken N.; Takahashi, Youtarou; Mogi, Masataka Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12245	journal	July 2016
Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations Giovannetti, Gianluca; Khomyakov, Petr A.; Brocks, Geert Physical Review B, Vol. 76, Issue 7 https://doi.org/10.1103/PhysRevB.76.073103	journal	August 2007
Multiple Magnetic Topological Phases in Bulk van der Waals Crystal ${MnSb}_{4} {Te}_{7}$ Huan, Shuchun; Zhang, Shihao; Jiang, Zhicheng Physical Review Letters, Vol. 126, Issue 24 https://doi.org/10.1103/PhysRevLett.126.246601	journal	June 2021
Nature of the Correlated Insulator States in Twisted Bilayer Graphene Xie, Ming; MacDonald, A. H. Physical Review Letters, Vol. 124, Issue 9 https://doi.org/10.1103/PhysRevLett.124.097601	journal	March 2020

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