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1

Karnaukhov, I. N. "Chern insulator with large Chern numbers. Chiral Majorana fermion liquid." Journal of Physics Communications 1, no. 5 (December 22, 2017): 051001. http://dx.doi.org/10.1088/2399-6528/aa9541.

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2

Zhou, P., C. Q. Sun, and L. Z. Sun. "Two Dimensional Antiferromagnetic Chern Insulator: NiRuCl6." Nano Letters 16, no. 10 (September 23, 2016): 6325–30. http://dx.doi.org/10.1021/acs.nanolett.6b02701.

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3

Zhang, Hongying, Xin Wang, Pan Zhou, Zengsheng Ma, and Lizhong Sun. "Two-dimensional ferromagnetic Chern insulator: WSe2 monolayer." Physics Letters A 402 (June 2021): 127344. http://dx.doi.org/10.1016/j.physleta.2021.127344.

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4

Liu, Chang, Yongchao Wang, Hao Li, Yang Wu, Yaoxin Li, Jiaheng Li, Ke He, Yong Xu, Jinsong Zhang, and Yayu Wang. "Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator." Nature Materials 19, no. 5 (January 6, 2020): 522–27. http://dx.doi.org/10.1038/s41563-019-0573-3.

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5

Tschirhart, C. L., M. Serlin, H. Polshyn, A. Shragai, Z. Xia, J. Zhu, Y. Zhang, et al. "Imaging orbital ferromagnetism in a moiré Chern insulator." Science 372, no. 6548 (May 27, 2021): 1323–27. http://dx.doi.org/10.1126/science.abd3190.

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Electrons in moiré flat band systems can spontaneously break time-reversal symmetry, giving rise to a quantized anomalous Hall effect. In this study, we use a superconducting quantum interference device to image stray magnetic fields in twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap, consistent with the expected contribution of chiral edge states to the magnetization of an orbital Chern insulator. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micrometer-scale domains pinned to structural disorder.
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6

LIN, HAI, and SHING-TUNG YAU. "ON EXOTIC SPHERE FIBRATIONS, TOPOLOGICAL PHASES, AND EDGE STATES IN PHYSICAL SYSTEMS." International Journal of Modern Physics B 27, no. 19 (July 15, 2013): 1350107. http://dx.doi.org/10.1142/s0217979213501075.

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We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n, respectively. They can be related to topological insulators, magnetoelectric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI′ heterostructures, and periodic TI/SC/TI/SC′ heterostructures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.
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7

Ni, Xiaojuan, Wei Jiang, Huaqing Huang, Kyung-Hwan Jin, and Feng Liu. "Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice." Nanoscale 10, no. 25 (2018): 11901–6. http://dx.doi.org/10.1039/c8nr02651c.

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8

Xue, Y., J. Y. Zhang, B. Zhao, X. Y. Wei, and Z. Q. Yang. "Non-Dirac Chern insulators with large band gaps and spin-polarized edge states." Nanoscale 10, no. 18 (2018): 8569–77. http://dx.doi.org/10.1039/c8nr00201k.

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9

Zhao, Gan, Haimen Mu, Feng Liu, and Zhengfei Wang. "Folding Graphene into a Chern Insulator with Light Irradiation." Nano Letters 20, no. 8 (July 13, 2020): 5860–65. http://dx.doi.org/10.1021/acs.nanolett.0c01758.

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10

Ozawa, Ryo, Masafumi Udagawa, Yutaka Akagi, and Yukitoshi Motome. "Surface and interface effects on a magnetic Chern insulator." Journal of Physics: Conference Series 592 (March 18, 2015): 012130. http://dx.doi.org/10.1088/1742-6596/592/1/012130.

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11

Takane, Yositake. "Bulk–Boundary Correspondence in a Non-Hermitian Chern Insulator." Journal of the Physical Society of Japan 90, no. 3 (March 15, 2021): 033704. http://dx.doi.org/10.7566/jpsj.90.033704.

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12

Wang, Aizhu, Xiaoming Zhang, Yuanping Feng, and Mingwen Zhao. "Chern Insulator and Chern Half-Metal States in the Two-Dimensional Spin-Gapless Semiconductor Mn2C6S12." Journal of Physical Chemistry Letters 8, no. 16 (August 2017): 3770–75. http://dx.doi.org/10.1021/acs.jpclett.7b01187.

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13

He, Junjie, Xiao Li, Pengbo Lyu, and Petr Nachtigall. "Near-room-temperature Chern insulator and Dirac spin-gapless semiconductor: nickel chloride monolayer." Nanoscale 9, no. 6 (2017): 2246–52. http://dx.doi.org/10.1039/c6nr08522a.

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14

Lima, L. S. "Quantum entanglement in some topological insulator models." International Journal of Modern Physics B 33, no. 24 (September 30, 2019): 1950284. http://dx.doi.org/10.1142/s0217979219502849.

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Quantum entanglement is studied in the neighborhood of a topological transition in some topological insulator models such as the two-dimensional Qi–Wu–Zhang model or Chern insulator. The system describes electrons hopping in two-dimensional chains. For the one-dimensional model case, there exist staggered hopping amplitudes. Our results show a strong effect of sudden variation of the topological charge Q in the neighborhood of phase transition on quantum entanglement for all the cases analyzed.
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15

Ozawa, Ryo, Masafumi Udagawa, Yutaka Akagi, and Yukitoshi Motome. "Reconstruction of Chiral Edge States in a Magnetic Chern Insulator." Journal of the Physical Society of Japan 83, no. 7 (July 15, 2014): 073706. http://dx.doi.org/10.7566/jpsj.83.073706.

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16

Prychynenko, Diana, and Sebastian D. Huber. "Z2 slave-spin theory of a strongly correlated Chern insulator." Physica B: Condensed Matter 481 (January 2016): 53–58. http://dx.doi.org/10.1016/j.physb.2015.10.027.

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17

Chen, Guorui, Aaron L. Sharpe, Eli J. Fox, Ya-Hui Zhang, Shaoxin Wang, Lili Jiang, Bosai Lyu, et al. "Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice." Nature 579, no. 7797 (March 2020): 56–61. http://dx.doi.org/10.1038/s41586-020-2049-7.

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18

Polshyn, H., J. Zhu, M. A. Kumar, Y. Zhang, F. Yang, C. L. Tschirhart, M. Serlin, et al. "Electrical switching of magnetic order in an orbital Chern insulator." Nature 588, no. 7836 (November 23, 2020): 66–70. http://dx.doi.org/10.1038/s41586-020-2963-8.

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19

Gonçalves, Miguel, Pedro Ribeiro, and Eduardo V. Castro. "Dirac points merging and wandering in a model Chern insulator." EPL (Europhysics Letters) 124, no. 6 (January 7, 2019): 67003. http://dx.doi.org/10.1209/0295-5075/124/67003.

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20

Wu, Ya-Jie, Jing He, and Su-Peng Kou. "Topological mid-gap states of Chern insulator with flux-superlattice." EPL (Europhysics Letters) 105, no. 4 (February 1, 2014): 47002. http://dx.doi.org/10.1209/0295-5075/105/47002.

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21

LIU, LAN-FENG, and SU-PENG KOU. "TOPOLOGICAL QUANTUM PHASE TRANSITION BETWEEN QUANTUM SPIN HALL STATE AND QUANTUM ANOMALOUS HALL STATE." International Journal of Modern Physics B 25, no. 17 (July 10, 2011): 2323–40. http://dx.doi.org/10.1142/s0217979211100096.

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In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities, and the number of zero mode on a π-flux). We find that at the topological quantum phase transitions (TQPTs), the topological "order parameter" — spin Chern number will jump. And since the masses of the nodal fermions will change sign, the third derivative of ground-state energy is nonanalytic. In addition, we discuss the finite temperature properties and the stability of the TQPTs.
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22

Ge, Jun, Yanzhao Liu, Jiaheng Li, Hao Li, Tianchuang Luo, Yang Wu, Yong Xu, and Jian Wang. "High-Chern-number and high-temperature quantum Hall effect without Landau levels." National Science Review 7, no. 8 (April 30, 2020): 1280–87. http://dx.doi.org/10.1093/nsr/nwaa089.

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Abstract The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 started the research on topological quantum states and laid the foundation of topology in physics. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). Here, we report the experimental discovery of high-Chern-number QHE (C = 2) without Landau levels and C = 1 Chern insulator state displaying a nearly quantized Hall resistance plateau above the Néel temperature in MnBi2Te4 devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.
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23

Cai, Tianyi, Xiao Li, Fa Wang, Sheng Ju, Ji Feng, and Chang-De Gong. "Single-Spin Dirac Fermion and Chern Insulator Based on Simple Oxides." Nano Letters 15, no. 10 (September 2, 2015): 6434–39. http://dx.doi.org/10.1021/acs.nanolett.5b01791.

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24

Jaworowski, B., P. Kaczmarkiewicz, and A. Wójs. "Fermionic Moore-Read Fractional Chern Insulator in the Thin-Torus Limit." Acta Physica Polonica A 134, no. 4 (October 2018): 919–23. http://dx.doi.org/10.12693/aphyspola.134.919.

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25

Song, Juntao, Yan-Yang Zhang, Yuxian Li, and Qing-feng Sun. "Topological quantum transitions in a two-band Chern insulator withn= 2." Journal of Physics: Condensed Matter 27, no. 4 (January 8, 2015): 045601. http://dx.doi.org/10.1088/0953-8984/27/4/045601.

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26

Ovchinnikov, Dmitry, Xiong Huang, Zhong Lin, Zaiyao Fei, Jiaqi Cai, Tiancheng Song, Minhao He, et al. "Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi2Te4." Nano Letters 21, no. 6 (March 12, 2021): 2544–50. http://dx.doi.org/10.1021/acs.nanolett.0c05117.

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27

DENG, WeiYin, XueQin HUANG, JiuYang LU, and ZhengYou LIU. "Spin-Chern insulator induced by pseudospin-orbit coupling in phononic crystals." SCIENTIA SINICA Physica, Mechanica & Astronomica 51, no. 8 (July 5, 2021): 084321. http://dx.doi.org/10.1360/sspma-2021-0082.

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28

Li, Linyang, Xiangru Kong, Xin Chen, Jia Li, Biplab Sanyal, and François M. Peeters. "Monolayer 1T-LaN2: Dirac spin-gapless semiconductor of p-state and Chern insulator with a high Chern number." Applied Physics Letters 117, no. 14 (October 5, 2020): 143101. http://dx.doi.org/10.1063/5.0023531.

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29

Wang, Yihua. "Broken-symmetry states in topological insulators." Modern Physics Letters B 29, no. 25 (September 20, 2015): 1530006. http://dx.doi.org/10.1142/s0217984915300069.

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Breaking the time-reversal symmetry (TRS) on the surface of a three-dimensional topological insulator (TI) transforms its metallic surface into a Chern insulator. The TRS-broken surface states are essential for many exotic emergent particles in condensed matter. In this review, I will show broken TRS surface states of TI induced by magnetism and by light imaged with scanning microscopy and photoemission spectroscopy, respectively. Our capability to manipulate mesoscopic magnetic structures as well as to shape ultrafast light pulses makes broken-symmetry states in TI promising platforms to simulate elusive fundamental particles such as magnetic monopoles and Majorana fermions.
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30

MARCHETTI, P. A., Z. B. SU, and L. YU. "METAL-INSULATOR CROSSOVER IN HIGH Tc CUPRATES: GAUGE FIELD THEORY VERSUS EXPERIMENTS." International Journal of Modern Physics B 16, no. 20n22 (August 30, 2002): 3199–202. http://dx.doi.org/10.1142/s0217979202013948.

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The U(1)×SU(2) Chern-Simons gauge field theory, proposed by the authors to explain in a unified fashion the metal-insulator crossover of the in-plane resistivity upon temperature decrease in heavily underdoped cuprates without magnetic field and a similar phenomenon, observed in several classes of superconducting cuprates, when a strong magnetic field suppresses the superconductivity, is briefly outlined and confronted with recent experiments.
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31

Li, Shan, Jing Yu, and Jing He. "Magnetic properties on Chern insulator of checkerboard lattice with topological flat band." Physics Letters A 384, no. 21 (July 2020): 126425. http://dx.doi.org/10.1016/j.physleta.2020.126425.

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32

Wang, Yi-Xiang, and Jie Cao. "Hubbard interaction in the arbitrary Chern number insulator: A mean-field study." Physics Letters A 381, no. 18 (May 2017): 1615–19. http://dx.doi.org/10.1016/j.physleta.2017.03.018.

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33

Chen, Guorui, Aaron L. Sharpe, Eli J. Fox, Ya-Hui Zhang, Shaoxin Wang, Lili Jiang, Bosai Lyu, et al. "Publisher Correction: Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice." Nature 581, no. 7807 (April 28, 2020): E3. http://dx.doi.org/10.1038/s41586-020-2237-5.

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34

Hermanns, Maria, Yann Salimi, Masudul Haque, and Lars Fritz. "Entanglement spectrum and entanglement Hamiltonian of a Chern insulator with open boundaries." Journal of Statistical Mechanics: Theory and Experiment 2014, no. 10 (October 21, 2014): P10030. http://dx.doi.org/10.1088/1742-5468/2014/10/p10030.

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35

Novokshonov, Sergey. "Quantization of the anomalous Hall conductance in a disordered magnetic Chern insulator." Journal of Physics: Conference Series 1389 (November 2019): 012104. http://dx.doi.org/10.1088/1742-6596/1389/1/012104.

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36

Mondal, Sayan, Priyadarshini Kapri, Bashab Dey, Tarun Kanti Ghosh, and Saurabh Basu. "Topological phase transition induced by band structure modulation in a Chern insulator." Journal of Physics: Condensed Matter 33, no. 22 (May 5, 2021): 225504. http://dx.doi.org/10.1088/1361-648x/abe798.

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37

Shin, Dongbin, Shunsuke A. Sato, Hannes Hübener, Umberto De Giovannini, Jeongwoo Kim, Noejung Park, and Angel Rubio. "Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states." Proceedings of the National Academy of Sciences 116, no. 10 (February 14, 2019): 4135–40. http://dx.doi.org/10.1073/pnas.1816904116.

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Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously used in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to obtain the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: The cell-averaged current density reveals the anomalous velocities that lead to the conductivity quantum. Results for prototypical cases are shown, including a spin-frozen valley Hall and a quantum anomalous Hall insulator. The advantage of this method is best illustrated by the example of a quantum spin Hall insulator: The quantized spin Hall conductivity is straightforwardly obtained irrespective of the non-Abelian nature in its Berry curvature. Moreover, the method can be extended to the description of real observables in nonequilibrium states of topological materials.
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38

Zeng, Ran, Fangfang Chen, Chi Wang, Mingyue Zhang, Haozhen Li, Qiliang Li, Jun Ou, Yaping Yang, and Shiyao Zhu. "Optical reflection properties for the interface associated with Chern insulator and chiral metamaterial." Physics Letters A 383, no. 30 (October 2019): 125920. http://dx.doi.org/10.1016/j.physleta.2019.125920.

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39

Regnault, N., and B. Andrei Bernevig. "Fractional Chern Insulator." Physical Review X 1, no. 2 (December 2, 2011). http://dx.doi.org/10.1103/physrevx.1.021014.

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40

He, Li, Zachariah Addison, Jicheng Jin, Eugene J. Mele, Steven G. Johnson, and Bo Zhen. "Floquet Chern insulators of light." Nature Communications 10, no. 1 (September 13, 2019). http://dx.doi.org/10.1038/s41467-019-12231-4.

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Abstract Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.
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41

Thonhauser, T., and David Vanderbilt. "Insulator/Chern-insulator transition in the Haldane model." Physical Review B 74, no. 23 (December 20, 2006). http://dx.doi.org/10.1103/physrevb.74.235111.

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42

Coh, Sinisa, and David Vanderbilt. "Electric Polarization in a Chern Insulator." Physical Review Letters 102, no. 10 (March 13, 2009). http://dx.doi.org/10.1103/physrevlett.102.107603.

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43

Ulčakar, Lara, Jernej Mravlje, and Tomaž Rejec. "Slow quenches in Chern insulator ribbons." Physical Review B 100, no. 12 (September 3, 2019). http://dx.doi.org/10.1103/physrevb.100.125110.

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44

Wu, H. C., L. Jin, and Z. Song. "Inversion symmetric non-Hermitian Chern insulator." Physical Review B 100, no. 15 (October 8, 2019). http://dx.doi.org/10.1103/physrevb.100.155117.

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45

Liu, Chang, Yongchao Wang, Ming Yang, Jiahao Mao, Hao Li, Yaoxin Li, Jiaheng Li, et al. "Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator." Nature Communications 12, no. 1 (July 30, 2021). http://dx.doi.org/10.1038/s41467-021-25002-x.

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AbstractThe intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = −1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.
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46

Verdeny, Albert, and Florian Mintert. "Tunable Chern insulator with optimally shaken lattices." Physical Review A 92, no. 6 (December 9, 2015). http://dx.doi.org/10.1103/physreva.92.063615.

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47

Jha, Vibhuti Bhushan, Garima Rani, and R. Ganesh. "Impurity-induced current in a Chern insulator." Physical Review B 95, no. 11 (March 27, 2017). http://dx.doi.org/10.1103/physrevb.95.115434.

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48

Barkeshli, M., N. Y. Yao, and C. R. Laumann. "Continuous Preparation of a Fractional Chern Insulator." Physical Review Letters 115, no. 2 (July 7, 2015). http://dx.doi.org/10.1103/physrevlett.115.026802.

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49

Chen, Hua, Xiong-Jun Liu, and X. C. Xie. "Chern Kondo Insulator in an Optical Lattice." Physical Review Letters 116, no. 4 (January 26, 2016). http://dx.doi.org/10.1103/physrevlett.116.046401.

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50

Maciejko, Joseph, and Andreas Rüegg. "Topological order in a correlated Chern insulator." Physical Review B 88, no. 24 (December 2, 2013). http://dx.doi.org/10.1103/physrevb.88.241101.

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