磁性拓扑绝缘体中的量子输运现象

刘畅; 王亚愚

doi:10.7498/aps.72.20230690

摘要

磁性拓扑绝缘体是过去十年里凝聚态物理学领域的一个重要研究方向, 其拓扑非平庸能带结构与自旋、轨道、电荷、维度等自由度之间的相互作用可以产生丰富的拓扑量子物态和拓扑相变现象. 对磁性拓扑绝缘体输运性质的研究是探索其新奇物性的重要手段, 对于深入理解拓扑量子物态以及开发新型低功耗电子学器件具有重要意义. 本文回顾了近年来磁性拓扑绝缘体输运实验方面的重要研究进展, 包括磁性掺杂拓扑绝缘体中的量子反常霍尔效应和拓扑量子相变现象、本征反铁磁拓扑绝缘体MnBi₂Te₄中的量子反常霍尔相、轴子绝缘体相和陈绝缘体相, 以及在脉冲强磁场下陈绝缘体演化出的螺旋式拓扑物态. 最后, 本文对未来磁性拓扑绝缘体研究的方向和该体系中尚未充分理解的输运现象进行了分析和展望.

关键词:

Abstract

In the past decade, magnetic topological insulators have been an important focus in condensed matter physics research. The intricate interplay between the nontrivial band topology and spin, orbit, charge, and dimensionality degrees of freedom can give rise to abundant exotic topological quantum states and topological phase transitions. Measuring the transport properties of magnetic topological insulators is a crucial approach to exploring their exotic properties, which is of significant scientific importance in deepening our understanding of topological quantum states. Simultaneously, it also holds substantial potential applications in the development of novel low-power electronic devices. In this work, experimental progress of transport researches of magnetic topological insulators is reviewed, including quantum anomalous Hall effect and topological quantum phase transitions in magnetically doped topological insulators, the quantum anomalous Hall phase, axion insulator phase and Chern insulator phase in intrinsic antiferromagnetic topological insulator MnBi₂Te₄, as well as the helical phase emerged from the Chern insulator in pulsed high magnetic fields. Finally, this work analyzes the future direction of development in magnetic topological insulators, and the transport phenomena that have not been understood in these systems, offering an insight into and perspectives on the potential breakthroughs to be achieved in this area of research.

Keywords:

作者及机构信息

刘畅^1,2,
王亚愚^3,4,5

1.
中国人民大学物理系, 光电功能与微纳器件北京市重点实验室, 北京　100872

2.
中国人民大学, 量子态构筑与调控教育部重点实验室, 北京　100872

3.
清华大学物理系, 低维量子物理国家重点实验室, 北京　100084

4.
量子信息前沿科学中心, 北京　100084

5.
合肥国家实验室, 合肥　230088

通信作者: 刘畅, liuchang_phy@ruc.edu.cn

基金项目: 国家自然科学基金(批准号: 12274453)和科技创新2030重大项目(批准号: 2021ZD0302502)资助的课题.

Authors and contacts

Liu Chang^1,2,
Wang Ya-Yu^3,4,5

1.
Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-Nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China

2.
Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China

3.
State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China

4.
Frontier Science Center for Quantum Information, Beijing 100084, China

5.
Hefei National Laboratory, Hefei 230088, China

Corresponding author: Liu Chang, liuchang_phy@ruc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12274453) and the Innovation Program for Quantum Science and Technology, China (Grant No. 2021ZD0302502).

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参考文献

[1]	Klitzing K v, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[2]	Klitzing K v 1986 Rev. Mod. Phys. 58 519 Google Scholar
[3]	Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559 Google Scholar
[4]	Thouless D J, Kohmoto M, Nightingale M P, Dennijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[5]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[6]	Haldane F D M 2017 Rev. Mod. Phys. 89 040502 Google Scholar
[7]	Onoda M, Nagaosa N 2003 Phys. Rev. Lett. 90 206601 Google Scholar
[8]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[9]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[10]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[11]	Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802 Google Scholar
[12]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[13]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[14]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803 Google Scholar
[15]	Qi X L, Hughes T L, Zhang S C 2008 Phys. Rev. B 78 195424 Google Scholar
[16]	Niemi A J, Semenoff G W 1983 Phys. Rev. Lett. 51 2077 Google Scholar
[17]	Semenoff G W 1984 Phys. Rev. Lett. 53 2449 Google Scholar
[18]	Fradkin E, Dagotto E, Boyanovsky D 1986 Phys. Rev. Lett. 57 2967 Google Scholar
[19]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[20]	Nomura K, Nagaosa N 2011 Phys. Rev. Lett. 106 166802 Google Scholar
[21]	Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802 Google Scholar
[22]	Wilczek F 1987 Phys. Rev. Lett. 58 1799 Google Scholar
[23]	Li R D, Wang J, Qi X L, Zhang S C 2010 Nat. Phys. 6 284 Google Scholar
[24]	Qi X L, Witten E, Zhang S C 2013 Phys. Rev. B 87 134519
[25]	Wang J, Lian B, Zhang S C 2016 Phys. Rev. B 93 045115
[26]	Zirnstein H G, Rosenow B 2017 Phys. Rev. B 96 201112(R
[27]	Wang J, Lian B, Qi X L, Zhang S C 2015 Phys. Rev. B 92 081107 Google Scholar
[28]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
[29]	Zhou Z H, Chien Y J, Uher C 2006 Phys. Rev. B 74 224418 Google Scholar
[30]	Hor Y S, Roushan P, Beidenkopf H, Seo J, Qu D, Checkelsky J G, Wray L A, Hsieh D, Xia Y, Xu S Y, Qian D, Hasan M Z, Ong N P, Yazdani A, Cava R J 2010 Phys. Rev. B 81 195203 Google Scholar
[31]	Checkelsky J G, Ye J T, Onose Y, Iwasa Y, Tokura Y 2012 Nat. Phys. 8 729 Google Scholar
[32]	Zhang D M, Richardella A, Rench D W, Xu S Y, Kandala A, Flanagan T C, Beidenkopf H, Yeats A L, Buckley B B, Klimov P V, Awschalom D D, Yazdani A, Schiffer P, Hasan M Z, Samarth N 2012 Phys. Rev. B 86 205127 Google Scholar
[33]	Chang C Z, Zhang J S, Liu M H, Zhang Z C, Feng X, Li K, Wang L L, Chen X, Dai X, Fang Z, Qi X L, Zhang S C, Wang Y Y, He K, Ma X C, Xue Q K 2013 Adv. Mater. 25 1065 Google Scholar
[34]	Kou X F, Lang M R, Fan Y B, Jiang Y, Nie T X, Zhang J M, Jiang W J, Wang Y Y, Yao Y G, He L, Wang K L 2013 Acs Nano 7 9205 Google Scholar
[35]	Chang C Z, Zhang J S, Feng X, Shen J, Zhang Z C, Guo M H, Li K, Ou Y B, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S H, Chen X, Jia J F, Dai X, Fang Z, Zhang S C, He K, Wang Y Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[36]	Checkelsky J G, Yoshimi R, Tsukazaki A, Takahashi K S, Kozuka Y, Falson J, Kawasaki M, Tokura Y 2014 Nat. Phys. 10 731 Google Scholar
[37]	Kou X, Guo S T, Fan Y, Pan L, Lang M, Jiang Y, Shao Q, Nie T, Murata K, Tang J, Wang Y Y, He L, Lee T K, Lee W L, Wang K L 2014 Phys. Rev. Lett. 113 137201 Google Scholar
[38]	Chang C Z, Zhao W, Kim D Y, Zhang H, Assaf B A, Heiman D, Zhang S C, Liu C, Chan M H, Moodera J S 2015 Nat. Mater. 14 473 Google Scholar
[39]	Mogi M, Yoshimi R, Tsukazaki A, Yasuda K, Kozuka Y, Takahashi K S, Kawasaki M, Tokura Y 2015 Appl. Phys. Lett. 107 182401
[40]	Ou Y B, Liu C, Jiang G Y, Feng Y, Zhao D Y, Wu W X, Wang X X, Li W, Song C L, Wang L L, Wang W B, Wu W D, Wang Y Y, He K, Ma X C, Xue Q K 2018 Adv. Mater. 30 1703062 Google Scholar
[41]	Lee I, Kim C K, Lee J, Billinge S J L, Zhong R D, Schneeloch J A, Liu T S, Valla T, Tranquada J M, Gu G D, Davis J C S 2015 Proc. Natl. Acad. Sci. U. S. A. 112 1316 Google Scholar
[42]	Lachman E O, Young A F, Richardella A, et al. 2015 Sci. Adv. 1 e1500740 Google Scholar
[43]	Wang W B, Ou Y B, Liu C, Wang Y Y, He K, Xue Q K, Wu W D 2018 Nat. Phys. 14 791 Google Scholar
[44]	Yue Z, Raikh M E 2016 Phys. Rev. B 94 155313 Google Scholar
[45]	Xing Y X, Xu F M, Cheung K T, Sun Q F, Wang J, Yao Y G 2018 New J. Phys. 20 043011 Google Scholar
[46]	Chen C Z, Liu H, Xie X C 2019 Phys. Rev. Lett. 122 026601 Google Scholar
[47]	Haim A, Ilan R, Alicea J 2019 Phys. Rev. Lett. 123 046801 Google Scholar
[48]	Kudla S, Dyrdal A, Dugaev V K, Berakdar J, Barnas J 2019 Phys. Rev. B 100 205428 Google Scholar
[49]	Otrokov M M, Menshchikova T V, Rusinov I P, Vergniory M G, Kuznetsov V M, Chulkov E V 2017 Jetp. Lett. 105 297 Google Scholar
[50]	Otrokov M M, Menshchikova T V, Vergniory M G, Rusinov I P, Vyazovskaya A Y, Koroteev Y M, Bihlmayer G, Ernst A, Echenique P M, Arnau A, Chulkov E V 2017 2D Mater 4 025082 Google Scholar
[51]	Gong Y, Guo J W, Li J H, et al. 2019 Chin. Phys. Lett. 36 076801 Google Scholar
[52]	Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, Xu Y 2019 Sci. Adv. 5 eaaw5685 Google Scholar
[53]	Otrokov M M, Klimovskikh I I, Bentmann H, et al. 2019 Nature 576 416 Google Scholar
[54]	Rienks E D L, Wimmer S, Sanchez-Barriga J, Caha O, Mandal P S, Ruzicka J, Ney A, Steiner H, Volobuev V V, Groiss H, Albu M, Kothleitner G, Michalicka J, Khan S A, Minar J, Ebert H, Bauer G, Freyse F, Varykhalov A, Rader O, Springholz G 2019 Nature 576 423 Google Scholar
[55]	Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401 Google Scholar
[56]	Deng Y, Yu Y, Shi M Z, Guo Z, Xu Z, Wang J, Chen X H, Zhang Y 2020 Science 367 895 Google Scholar
[57]	Liu C, Wang Y C, Li H, Wu Y, Li Y X, Li J H, He K, Xu Y, Zhang J S, Wang Y Y 2020 Nat. Mater. 19 522 Google Scholar
[58]	Ge J, Liu Y, Li J, Li H, Luo T, Wu Y, Xu Y, Wang J 2020 Natl. Sci. Rev. 7 1280 Google Scholar
[59]	Zhang R X, Wu F, Sarma S D 2020 Phys. Rev. Lett. 124 136407 Google Scholar
[60]	Zhang J, Liu Z, Wang J 2019 Phys. Rev. B 100 165117 Google Scholar
[61]	Li J, Wang C, Zhang Z, Gu B L, Duan W, Xu Y 2019 Phys. Rev. B 100 121103 Google Scholar
[62]	Bestwick A J, Fox E J, Kou X, Pan L, Wang K L, Goldhaber-Gordon D 2015 Phys. Rev. Lett. 114 187201 Google Scholar
[63]	Chang C Z, Zhao W, Kim D Y, Wei P, Jain J K, Liu C, Chan M H, Moodera J S 2015 Phys. Rev. Lett. 115 057206 Google Scholar
[64]	Feng Y, Feng X, Ou Y, Wang J, Liu C, Zhang L, Zhao D, Jiang G, Zhang S C, He K, Ma X, Xue Q K, Wang Y Y 2015 Phys. Rev. Lett. 115 126801 Google Scholar
[65]	Liu M, Wang W, Richardella A R, Kandala A, Li J, Yazdani A, Samarth N, Ong N P 2016 Sci. Adv. 2 e1600167 Google Scholar
[66]	Feng X, Feng Y, Wang J, Ou Y B, Hao Z Q, Liu C, Zhang Z C, Zhang L G, Lin C J, Liao J, Li Y Q, Wang L L, Ji S H, Chen X, Ma X C, Zhang S C, Wang Y Y, He K, Xue Q K 2016 Adv. Mater. 28 6386 Google Scholar
[67]	Chang C Z, Zhao W, Li J, Jain J K, Liu C, Moodera J S, Chan M H 2016 Phys. Rev. Lett. 117 126802 Google Scholar
[68]	Yasuda K, Wakatsuki R, Morimoto T, Yoshimi R, Tsukazaki A, Takahashi K S, Ezawa M, Kawasaki M, Nagaosa N, Tokura Y 2016 Nat. Phys. 12 555 Google Scholar
[69]	Liu C, Zang Y Y, Ruan W, Gong Y, He K, Ma X C, Xue Q K, Wang Y Y 2017 Phys. Rev. Lett. 119 176809 Google Scholar
[70]	Mogi M, Kawamura M, Tsukazaki A, Yoshimi R, Takahashi K S, Kawasaki M, Tokura Y 2017 Sci. Adv. 3 eaao1669 Google Scholar
[71]	Mogi M, Kawamura M, Yoshimi R, Tsukazaki A, Kozuka Y, Shirakawa N, Takahashi K S, Kawasaki M, Tokura Y 2017 Nat. Mater. 16 516 Google Scholar
[72]	Xiao D, Jiang J, Shin J H, Wang W, Wang F, Zhao Y F, Liu C, Wu W, Chan M H W, Samarth N, Chang C Z 2018 Phys. Rev. Lett. 120 056801 Google Scholar
[73]	Watanabe R, Yoshimi R, Kawamura M, Mogi M, Tsukazaki A, Yu X Z, Nakajima K, Takahashi K S, Kawasaki M, Tokura Y 2019 Appl. Phys. Lett. 115 102403 Google Scholar
[74]	Otrokov M M, Rusinov I P, Blanco-Rey M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, Chulkov E V 2019 Phys. Rev. Lett. 122 107202 Google Scholar
[75]	Yan J Q, Zhang Q, Heitmann T, Huang Z, Chen K Y, Cheng J G, Wu W, Vaknin D, Sales B C, McQueeney R J 2019 Phys. Rev. Mater. 3 064202 Google Scholar
[76]	Zhang S, Wang R, Wang X, Wei B, Chen B, Wang H, Shi G, Wang F, Jia B, Ouyang Y, Xie F, Fei F, Zhang M, Wang X, Wu D, Wan X, Song F, Zhang H, Wang B 2020 Nano Lett. 20 709 Google Scholar
[77]	Liu C, Ou Y B, Feng Y, Jiang G Y, Wu W X, Li S R, Cheng Z J, He K, Ma X C, Xue Q K, Wang Y Y 2020 Phys. Rev. X 10 041063
[78]	Liu C, Wang Y C, Yang M, Mao J H, Li H, Li Y X, Li J H, Zhu H P, Wang J F, Li L, Wu Y, Xu Y, Zhang J S, Wang Y Y 2021 Nat. Commun. 12 4647 Google Scholar
[79]	Qiu J X, Tzschaschel C, Ahn J, Gao A, Li H, Zhang X Y, Ghosh B, Hu C, Wang Y X, Liu Y F, Berube D, Dinh T, Gong Z, Lien S W, Ho S C, Singh B, Watanabe K, Taniguchi T, Bell D C, Lu H Z, Bansil A, Lin H, Chang T R, Zhou B B, Ma Q, Vishwanath A, Ni N, Xu S Y 2023 Nat. Mater. 22 583 Google Scholar
[80]	Okazaki Y, Oe T, Kawamura M, Yoshimi R, Nakamura S, Takada S, Mogi M, Takahashi K S, Tsukazaki A, Kawasaki M, Tokura Y, Kaneko N H 2022 Nat. Phys. 18 25 Google Scholar
[81]	Gao A, Liu Y F, Hu C, Qiu J X, et al. 2021 Nature 595 521 Google Scholar
[82]	Mogi M, Okamura Y, Kawamura M, Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Morimoto T, Nagaosa N, Kawasaki M, Takahashi Y, Tokura Y 2022 Nat. Phys. 18 390 Google Scholar
[83]	Chen Y L, Analytis J G, Chu J H, Liu Z K, Mo S K, Qi X L, Zhang H J, Lu D H, Dai X, Fang Z, Zhang S C, Fisher I R, Hussain Z, Shen Z X 2009 Science 325 178 Google Scholar
[84]	Zhang Y, He K, Chang C Z, Song C L, Wang L L, Chen X, Jia J F, Fang Z, Dai X, Shan W Y, Shen S Q, Niu Q, Qi X L, Zhang S C, Ma X C, Xue Q K 2010 Nat. Phys. 6 584 Google Scholar
[85]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[86]	Zhang J S, Chang C Z, Zhang Z C, Wen J, Feng X, Li K, Liu M H, He K, Wang L L, Chen X, Xue Q K, Ma X C, Wang Y Y 2011 Nat. Commun. 2 574 Google Scholar
[87]	Liu Q, Liu C X, Xu C, Qi X L, Zhang S C 2009 Phys. Rev. Lett. 102 156603 Google Scholar
[88]	Sessi P, Reis F, Bathon T, Kokh K A, Tereshchenko O E, Bode M 2014 Nat. Commun. 5 5349 Google Scholar
[89]	Li M D, Chang C Z, Wu L J, Tao J, Zhao W W, Chan M H W, Moodera J S, Li J, Zhu Y M 2015 Phys. Rev. Lett. 114 146802 Google Scholar
[90]	Jiang J, Xiao D, Wang F, Shin J H, Andreoli D, Zhang J, Xiao R, Zhao Y F, Kayyalha M, Zhang L, Wang K, Zang J, Liu C, Samarth N, Chan M H W, Chang C Z 2020 Nat. Mater. 19 732 Google Scholar
[91]	Dziom V, Shuvaev A, Pimenov A, Astakhov G V, Ames C, Bendias K, Bottcher J, Tkachov G, Hankiewicz E M, Brune C, Buhmann H, Molenkamp L W 2017 Nat. Commun. 8 15197 Google Scholar
[92]	Okada K N, Takahashi Y, Mogi M, Yoshimi R, Tsukazaki A, Takahashi K S, Ogawa N, Kawasaki M, Tokura Y 2016 Nat. Commun. 7 12245 Google Scholar
[93]	Wu L, Salehi M, Koirala N, Moon J, Oh S, Armitage N P 2016 Science 354 1124 Google Scholar
[94]	He Q L, Hughes T L, Armitage N P, Tokura Y, Wang K L 2022 Nat. Mater. 21 15 Google Scholar
[95]	Mellnik A R, Lee J S, Richardella A, Grab J L, Mintun P J, Fischer M H, Vaezi A, Manchon A, Kim E A, Samarth N, Ralph D C 2014 Nature 511 449 Google Scholar
[96]	Kondou K, Yoshimi R, Tsukazaki A, Fukuma Y, Matsuno J, Takahashi K S, Kawasaki M, Tokura Y, Otani Y 2016 Nat. Phys. 12 1027 Google Scholar
[97]	Li C H, van 't Erve O M J, Robinson J T, Liu Y, Li L, Jonker B T 2014 Nat. Nanotechnol. 9 218 Google Scholar
[98]	Gotz M, Fijalkowski K M, Pesel E, Hartl M, Schreyeck S, Winnerlein M, Grauer S, Scherer H, Brunner K, Gould C, Ahlers F J, Molenkamp L W 2018 Appl. Phys. Lett. 112 072102 Google Scholar
[99]	Okazaki Y, Oe T, Kawamura M, Yoshimi R, Nakamura S, Takada S, Mogi M, Takahashi K S, Tsukazaki A, Kawasaki M, Tokura Y, Kaneko N H 2020 Appl. Phys. Lett. 116 143101
[100]	Fox E J, Rosen I T, Yang Y F, Jones G R, Elmquist R E, Kou X F, Pan L, Wang K L, Goldhaber-Gordon D 2018 Phys. Rev. B 98 075145 Google Scholar
[101]	Lee D S, Kim T H, Park C H, Chung C Y, Lim Y S, Seo W S, Park H H 2013 Crystengcomm 15 5532 Google Scholar
[102]	Sun H Y, Xia B W, Chen Z J, Zhang Y J, Liu P F, Yao Q S, Tang H, Zhao Y J, Xu H, Liu Q H 2019 Phys. Rev. Lett. 123 096401 Google Scholar
[103]	Wu J Z, Liu F C, Sasase M, Ienaga K, Obata Y, Yukawa R, Horiba K, Kumigashira H, Okuma S, Inoshita T, Hosono H 2019 Sci. Adv. 5 eaax9989 Google Scholar
[104]	Chen B, Fei F C, Zhang D Q, et al. 2019 Nat. Commun. 10 4469 Google Scholar
[105]	Li H, Gao S Y, Duan S F, et al. 2019 Phys. Rev. X 9 041039
[106]	Hao Y J, Liu P F, Feng Y, et al. 2019 Phys. Rev. X 9 041038
[107]	Chen Y J, Xu L X, Li J H, Li Y W, Zhang C F, Li H, Wu Y, Liang A J, Chen C, Jung S W, Cacho C, Wang H Y, Mao Y H, Liu S, Wang M X, Guo Y F, Xu Y, Liu Z K, Yang L X, Chen Y L 2019 Phys. Rev. X 9 041040
[108]	Swatek P, Wu Y, Wang L L, Lee K, Schrunk B, Yan J Q, Kaminski A 2020 Phys. Rev. B 101 161109 Google Scholar
[109]	Nevola D, Li H X, Yan J Q, Moore R G, Lee H N, Miao H, Johnson P D 2020 Phys. Rev. Lett. 125 117205 Google Scholar
[110]	Ovchinnikov D, Huang X, Lin Z, Fei Z Y, Cai J Q, Song T C, He M H, Jiang Q N, Wang C, Li H, Wang Y Y, Wu Y, Xiao D, Chu J H, Yan J Q, Chang C Z, Cui Y T, Xu X D 2021 Nano Lett. 21 2544 Google Scholar
[111]	Cai J Q, Ovchinnikov D, Fei Z Y, He M H, Song T C, Lin Z, Wang C, Cobden D, Chu J H, Cui Y T, Chang C Z, Xiao D, Yan J Q, Xu X D 2022 Nat. Commun. 13 1668 Google Scholar
[112]	Ying Z, Zhang S, Chen B, Jia B, Fei F, Zhang M, Zhang H, Wang X, Song F 2022 Phys. Rev. B 105 085412 Google Scholar
[113]	Yang S Q, Xu X L, Zhu Y Z, Niu R R, Xu C Q, Peng Y X, Cheng X, Jia X H, Huang Y, Xu X F, Lu J M, Ye Y 2021 Phys. Rev. X 11 011003
[114]	Cui J H, Shi M Z, Wang H H, Yu F H, Wu T, Luo X G, Ying J J, Chen X H 2019 Phys. Rev. B 99 155125 Google Scholar
[115]	Li H, Liu S, Liu C, Zhang J, Xu Y, Yu R, Wu Y, Zhang Y, Fan S 2020 Phys. Chem. Chem. Phys. 22 556 Google Scholar
[116]	Yan J-Q, Huang Z, Wu W, May A F 2022 J. Alloy Compd. 906 164327 Google Scholar
[117]	Hu C, Gao A, Berggren B S, Li H, Kurleto R, Narayan D, Zeljkovic I, Dessau D, Xu S, Ni N 2021 Phys. Rev. Mater. 5 124206 Google Scholar
[118]	Zhang J S, Chang C Z, Tang P Z, Zhang Z C, Feng X, Li K, Wang L L, Chen X, Liu C, Duan W, He K, Xue Q K, Ma X, Wang Y 2013 Science 339 1582 Google Scholar
[119]	Li B, Yan J Q, Pajerowski D M, Gordon E, Nedic A M, Sizyuk Y, Ke L Q, Orth P P, Vaknin D, McQueeney R J 2020 Phys. Rev. Lett. 124 167204 Google Scholar
[120]	Sass P M, Kim J, Vanderbilt D, Yan J Q, Wu W D 2020 Phys. Rev. Lett. 125 037201 Google Scholar
[121]	Sass P M, Ge W B, Yan J Q, Obeysekera D, Yang J J, Wu W D 2020 Nano Lett 20 2609 Google Scholar
[122]	Lai Y, Ke L Q, Yan J Q, McDonald R D, McQueeney R J 2021 Phys. Rev. B 103 184429 Google Scholar
[123]	Estyunin D A, Klimovskikh I I, Shikin A M, Schwier E F, Otrokov M M, Kimura A, Kumar S, Filnov S O, Aliev Z S, Babanly M B, Chulkov E V 2020 APL Mater 8 021105 Google Scholar
[124]	Li Y, Liu C, Wang Y, Lian Z, Li H, Wu Y, Zhang J, Wang Y 2023 Science Bulletin 68 1252
[125]	Shikin A M, Estyunin D A, Zaitsev N L, et al. 2021 Phys. Rev. B 104 115168 Google Scholar
[126]	Tan H, Yan B 2023 Phys. Rev. Lett. 130 126702 Google Scholar
[127]	Kivelson S, Lee D H, Zhang S C 1992 Phys. Rev. B 46 2223 Google Scholar
[128]	Hilke M, Shahar D, Song S H, Tsui D C, Xie Y H, Monroe D 1998 Nature 395 675 Google Scholar
[129]	Wong L W, Jiang H W, Trivedi N, Palm E 1995 Phys. Rev. B 51 18033 Google Scholar
[130]	Shahar D, Tsui D C, Shayegan M, Bhatt R N, Cunningham J E 1995 Phys. Rev. Lett. 74 4511 Google Scholar
[131]	Pan W, Shahar D, Tsui D C, Wei H P, Razeghi M 1997 Phys. Rev. B 55 15431 Google Scholar
[132]	Kou X F, Pan L, Wang J, Fan Y B, Choi E S, Lee W L, Nie T X, Murata K, Shao Q M, Zhang S C, Wang K L 2015 Nat. Commun. 6 8474 Google Scholar
[133]	Kawamura M, Mogi M, Yoshimi R, Tsukazaki A, Kozuka Y, Takahashi K S, Kawasaki M, Tokura Y 2018 Phys. Rev. B 98 140404(R
[134]	Wu X Y, Xiao D, Chen C Z, Sun J, Zhang L, Chan M H W, Samarth N, Xie X C, Lin X, Chang C Z 2020 Nat. Commun. 11 4532 Google Scholar
[135]	Kayyalha M, Xiao D, Zhang R X, Shin J, Jiang J, Wang F, Zhao Y F, Xiao R, Zhang L, Fijalkowski K M, Mandal P, Winnerlein M, Gould C, Li Q, Molenkamp L W, Chan M H W, Samarth N, Chang C Z 2020 Science 367 64 Google Scholar
[136]	Huang Y Y, Setiawan F, Sau J D 2018 Phys. Rev. B 97 100501(R
[137]	Ji W J, Wen X G 2018 Phys. Rev. Lett. 120 107002 Google Scholar
[138]	Wang J, Zhou Q, Lian B A, Zhang S C 2015 Phys. Rev. B 92 064520 Google Scholar
[139]	Lian B A, Wang J, Sun X Q, Vaezi A, Zhang S C 2018 Phys. Rev. B 97 125408 Google Scholar
[140]	Lian B, Sun X Q, Vaezi A, Qi X L, Zhang S C 2018 Proc. Natl. Acad. Sci. U. S. A. 115 10938 Google Scholar
[141]	Liu C, Zang Y Y, Gong Y, He K, Ma X C, Xue Q K, Wang Y Y 2022 Sci. China Phys. Mech. 65 266812 Google Scholar
[142]	Zhu J J, Yao D X, Zhang S C, Chang K 2011 Phys. Rev. Lett. 106 097201 Google Scholar
[143]	Xu Z M, Duan W H, Xu Y 2022 Nano Lett. 23 305
[144]	Li Y X, Liu C, Wang Y C, Li H, Wu Y, Zhang J S, Wang Y Y 2022 J. Phys. D Appl. Phys. 55 104001 Google Scholar
[145]	Marsh D J E, Fong K C, Lentz E W, Smejkal L, Ali M N 2019 Phys. Rev. Lett. 123 121601 Google Scholar
[146]	Nenno D M, Garcia C A C, Gooth J, Felser C, Narang P 2020 Nat. Rev. Phys. 2 682 Google Scholar
[147]	Sekine A, Nomura K 2021 J. Appl. Phys. 129 141101 Google Scholar
[148]	Li H L, Chen C Z, Jiang H, Xie X C 2021 Phys. Rev. Lett. 127 236402 Google Scholar
[149]	Roth A, Brune C, Buhmann H, Molenkamp L W, Maciejko J, Qi X L, Zhang S C 2009 Science 325 294 Google Scholar
[150]	Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[151]	Young A F, Sanchez-Yamagishi J D, Hunt B, Choi S H, Watanabe K, Taniguchi T, Ashoori R C, Jarillo-Herrero P 2014 Nature 505 528 Google Scholar
[152]	Veyrat L, Déprez C, Coissard A, Li X, Gay F, Watanabe K, Taniguchi T, Han Z, Piot B A, Sellier H, Sacépé B 2020 Science 367 781 Google Scholar
[153]	Chen R, Li S, Sun H P, Liu Q H, Zhao Y, Lu H Z, Xie X C 2021 Phys. Rev. B 103 L241409 Google Scholar
[154]	Gu M Q, Li J Y, Sun H Y, Zhao Y F, Liu C, Liu J P, Lu H Z, Liu Q H 2021 Nat. Commun. 12 3524 Google Scholar
[155]	Zhou H M, Li H L, Xu D H, Chen C Z, Sun Q F, Xie X C 2022 Phys. Rev. Lett. 129 096601 Google Scholar
[156]	Gong M, Liu H W, Jiang H, Chen C Z, Xie X C 2023 Natl. Sci. Rev. 10 nwad025 Google Scholar
[157]	Zou J Y, Fu B, Wang H W, Hu Z A, Shen S Q 2022 Phys. Rev. B 105 L201106 Google Scholar
[158]	Sun S, Weng H M, Dai X 2022 Phys. Rev. B 106 L241105 Google Scholar
[159]	Song Z D, Lian B A, Queiroz R, Ilan R, Bernevig B A, Stern A 2021 Phys. Rev. Lett. 127 016602
[160]	Wang J, Lian B, Zhang S C 2014 Phys. Rev. B 89 085106 Google Scholar
[161]	Liang S, Kushwaha S, Gao T, Hirschberger M, Li J, Wang Z, Stolze K, Skinner B, Bernevig B A, Cava R J, Ong N P 2019 Nat. Mater. 18 443 Google Scholar
[162]	Bottcher J, Tutschku C, Hankiewicz E M 2020 Phys. Rev. B 101 195433 Google Scholar
[163]	Bottcher J, Tutschku C, Molenkamp L W, Hankiewicz E M 2019 Phys. Rev. Lett. 123 226602 Google Scholar
[164]	Lian B, Liu Z C, Zhang Y B, Wang J 2020 Phys. Rev. Lett. 124 126402

施引文献

图 1 磁性拓扑绝缘体中关于拓扑量子物态和拓扑相变研究的关键进展时间线

Fig. 1. Timeline of the key developments in the studies of topological quantum state and topological phase transition in magnetic TIs.

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图 2 磁性拓扑绝缘体结构示意图　(a)磁性掺杂拓扑绝缘体Mn_xBi_2–xTe₃晶格结构和磁结构, 红色箭头表示随机分布磁矩的磁化方向; (b)本征反铁磁拓扑绝缘体MnBi₂Te₄的晶格结构和磁结构, 红色和绿色箭头表示层间反平行排列磁矩的磁化方向

Fig. 2. Schematic layer structure of magnetic topological insulators (TIs): (a) Crystal and magnetic structures of magnetically doped TI Mn_xBi_2–xTe₃, the red arrows represent the magnetizations of the randomly distributed magnetic moments; (b) crystal and magnetic structures of the intrinsic AFM TI MnBi₂Te₄. The red and green arrows denote the magnetization of the oppositely aligned magnetic moments between neighboring layers.

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图 3 MnBi₂Te₄块体和薄膜的基本表征　(a)磁化(沿着c轴方向)和电阻随着温度变化曲线; (b)在2 K温度下, 厚度为4 SL到8 SL的薄膜的反射型磁圆二向色谱信号随着磁场的变化; (c)由拓扑表面态形成的线性狄拉克锥色散关系以及其在狄拉克点附近的放大图; 图(a)和(c)来自文献[107], 图(b)来自文献[110]

Fig. 3. Basic characterization of MnBi₂Te₄ bulk crystal and thin flakes: (a) Magnetization (with magnetic field applied along c axis) and resistance as functions of T; (b) reflective magnetic circular dichroism (RCMD) measurements as a function of magnetic field for 4 SL to 8 SL flakes at T = 2 K; (c) linear band dispersion with a clear Dirac cone formed by surface states and the enlarged plot of the dispersion near the Dirac point; (a) and (c) are adopted from Ref.[107], (b) is adopted from Ref.[110].

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图 4 磁性掺杂拓扑绝缘体中的量子反常霍尔效应 (a), (b) 5-QL厚Cr_0.15(Bi_0.1Sb_0.9)_1.85Te₃中不同栅极电压下霍尔电阻率ρ_yx和纵向电阻率ρ_xx随着磁场的变化; (c)零磁场下霍尔电阻率ρ_yx(0)(蓝色空心方块)和纵向电阻率ρ_xx(0)(红色空心圆形)随栅压变化, 以上数据在30 mK温度下采集; (d), (e) 5-QL厚(Cr_0.16V_0.84)_0.19(Bi_0.1Sb_0.9)_1.81Te₃在电荷中性点处霍尔电阻率ρ_yx和纵向电阻率ρ_xx随着磁场的变化; (f)零磁场下霍尔电阻率ρ_yx(0)(蓝色实线)和纵向电阻率ρ_xx(0)(红色实线)随栅压变化, 以上数据在300 mK温度下采集. 图(a)—(c)来自文献[35], 图(d)—(f)来自文献[40]

Fig. 4. The optimization of the QAH effect in magnetically doped TIs. (a), (b) Magnetic field dependences of ρ_yx and ρ_xx at different V_g in a 5-QL Cr_0.15(Bi_0.1Sb_0.9)_1.85Te₃ film; (c) dependence of ρ_yx(0) (empty blue squares) and ρ_xx(0) (empty red circles) on V_g, all the above data was measured at T = 30 mK; (d), (e) magnetic field dependences of ρ_yx and ρ_xx at the charge neutrality point in a 5-QL (Cr_0.16V_0.84)_0.19(Bi_0.1Sb_0.9)_1.81Te₃ thin film; (f) dependence of ρ_yx(0) (blue line) and ρ_xx(0) (red line) on V_g. All the data in the Cr- and V-codoped TI was measured at T = 300 mK. (a)–(c) are adopted from Ref.[35], (d)–(f) are adopted Ref.[40].

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图 5 磁无序引起的不同量子反常霍尔基态　(a), (b)处于量子反常霍尔相和反常霍尔绝缘体相的两块磁性掺杂拓扑绝缘体的霍尔电阻率ρ_yx和纵向电阻率ρ_xx随着磁场的变化, 两块样品的化学组成分别是(Cr_0.16V_0.84)_0.19(Bi_0.1Sb_0.9)_1.81Te₃和Cr_0.23(Bi_0.4Sb_0.6)_1.77Te₃; (c)从82块样品中总结出的峰值纵向电阻率$ \rho _{xx}^{H{\text{c}}} $和零磁场纵向电阻率$ \rho _{xx}^0 $之间的关系; (d)处于反常霍尔绝缘体相的样品在不同温度下ρ_xx随磁场变化曲线; (e)从图(d)中提取出的不同磁场下ρ_xx随着温度的演化; (f)量子临界点附近关于ρ_xx的标度行为分析. 当临界指数κ取0.31时所有数据都重合在一条曲线上. 图片来自文献[77]

Fig. 5. Distinct QAH ground states induced by magnetic disorder: (a), (b) Magnetic field dependent ρ_yx and ρ_xx for magnetically doped TIs in the ground states of QAH state and the AH insulator state, respectively, the chemical compositions of the two magnetically doped TIs are (Cr_0.16V_0.84)_0.19(Bi_0.1Sb_0.9)_1.81Te₃ and Cr_0.23(Bi_0.4Sb_0.6)_1.77Te₃; (c) relationship between peak value of longitudinal resistivity $ \rho _{xx}^{H{\text{c}}} $ and zero field longitudinal resistivity $ \rho _{xx}^0 $ summarized from the transport results of 82 magnetic TIs; (d) magnetic field dependent ρ_xx at different T in an AH insulator sample; (e) T-dependent ρ_xx extracted from (d) at different magnetic fields; (f) finite size scaling analysis of ρ_xx in the vicinity of the quantum critical point, all the curves collapse together for the critical exponent κ~ 0.31. The figures are adopted from Ref. [77].

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图 6 两种不同手性的反常霍尔效应　(a)具有逆时针手性的反常霍尔效应回滞曲线, 当磁化方向为正时反常霍尔电阻率$ \rho _{yx}^0 $ 符号为“+”; (b)具有顺时针手性的反常霍尔效应回滞曲线, 当磁化方向为正时反常霍尔电阻率$ \rho _{yx}^0 $ 符号为“–”; (c), (d)不同磁性掺杂拓扑绝缘体中狄拉克点能隙打开示意图, 对于Mn掺杂体系, 巡游电子自旋方向与Mn²⁺离子3d轨道占据态电子自旋方向相反, 对于Cr掺杂体系, 巡游电子自旋方向与Cr³⁺离子3d轨道占据态电子自旋方向相同. 图片来自文献^[141]

Fig. 6. AH effect with different chirality: (a) AH effect hysteresis with counter-clockwise chirality, the AH resistivity $ \rho _{yx}^0 $ is “+” when the magnetization is positive; (b) AH effect hysteresis with clockwise chirality, the AH resistivity $ \rho _{yx}^0 $ is “–” when the magnetization is positive; (c), (d) schematic illustrations of the Dirac gap opening process in different magnetic TI systems, for Mn-doped system, the spin of itinerant electrons is antiparallel to the spin of the 3d electrons in the occupied states in Mn²⁺ ions. Whereas for Cr-doped system, the spin of itinerant electrons is parallel to the spin of the 3d electrons in the occupied states in Cr³⁺ ions. The figures are adopted from Ref. [141].

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图 7 厚度为5-SL的MnBi₂Te₄样品中观测到的量子反常霍尔效应 (a), (b)在1.4 K温度下霍尔电阻R_yx和纵向电阻R_xx随着磁场的变化曲线, 在零磁场条件下, 霍尔电阻达到0.97h/e², 纵向电阻降至0.061h/e². 在磁场超过2.5 T条件下, 量子化程度被提升至R_yx ~ 0.998h/e²; (c)通过纵向电阻数值随1/T变化的Arrhenius拟合获得的能隙随着磁场的变化曲线. 图片来自文献[56]

Fig. 7. QAH effect in a five-layer MnBi₂Te₄ flake: (a), (b) Magnetic field dependent R_yx and R_xx acquired at 1.4 K. R_yx reaches 0.97h/e² concomitant with R_xx of 0.061h/e² at zero magnetic field, under magnetic field above 2.5 T, the QAH quantization is improved to R_yx ~ 0.998h/e²; (c) energy gap as a function of magnetic field extracted from fitting the Arrhenius plots of R_xx as a function of 1/T. The figures are adopted from Ref. [56].

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图 8 厚度为6-SL的MnBi₂Te₄在不同电压下的输运行为　(a), (b)在1.6 K温度时不同栅压下霍尔电阻率ρ_yx和纵向电阻率ρ_xx随着磁场的变化曲线, 当费米能级被调节到带隙中时(22 V ≤ V_g ≤ 30 V, 如蓝色区间所示), 零磁场巨大的纵向电阻率和很宽的零级霍尔平台揭示了轴子绝缘相存在的重要证据, 在高磁场下, 量子化的霍尔电阻平台和消失的纵向电阻率表明系统进入陈绝缘体相; (b)零磁场纵向电阻率ρ_xx和霍尔电阻率ρ_yx在磁场下的斜率随着栅极电压变化图; (c) 磁场–9 T时纵向电阻率ρ_xx和霍尔电阻率ρ_yx随着栅极电压变化图; (d)轴子绝缘体相和陈绝缘体相磁结构和电子结构示意图. 图片来自文献[57]

Fig. 8. Gate dependent transport properties in a six-layer MnBi₂Te₄: (a) Magnetic field dependence of ρ_yx and ρ_xx at different gate voltages at T = 1.6 K, when Fermi level E_F lies within the band gap for 22 V ≤ V_g ≤ 30 V (blue square envelope), both the large longitudinal resistivity ρ_xx and wide zero Hall plateau are key signatures of the axion insulator state, at high magnetic field, the nearly quantized Hall plateau and vanishing ρ_xx are characteristics of a Chern insulator; (b) the V_g dependence of ρ_xx and the slope of ρ_yx vs. H measured at T = 1.6 K around zero magnetic field; (c) the evolution of ρ_xx and ρ_yx as a function V_g at T = 1.6 K and μ₀H = –9 T, which reveals the Chern insulator state; (d) the schematic pictures of the magnetic order and electronic structure of the axion insulator and Chern insulator state. The figures are adopted from Ref. [57].

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图 9 磁场极化的铁磁MnBi₂Te₄中高陈数量子化现象 (a), (b)厚度为10-SL 样品在2—15 K条件下霍尔电阻R_yx和纵向电阻R_xx随着磁场的变化. 在温度为13 K时霍尔电阻R_yx可以达到0.97h/e²; (c)—(e)厚度为7-SL的双栅极MnBi₂Te₄器件在不同载流子浓度下n_1–3霍尔电阻率ρ_yx随磁场的变化; (f)—(h)纵向电阻率ρ_xx随磁场的变化, 在载流子浓度为n₂时, 超过10 T的磁场可以引起了C = –2的高陈数的量子化现象, 其霍尔电阻率ρ_yx为0.5h/e², 纵向电阻率ρ_xx为0.05h/e². 图(a)和(b)来自文献[58], 图(c)—(h)来自文献[111]

Fig. 9. Chern insulator quantization with high Chern number in magnetic-field polarized FM MnBi₂Te₄: (a), (b) R_yx and R_xx as a function of magnetic field at different T_s from 2 K to 15 K in a 10-SL sample, the Hall quantization can reach 0.97h/e² at 13 K; (c)–(e) ρ_yx as a function of magnetic field under varied carrier density n_1–3 for a 7-SL dual gated MnBi₂Te₄ devices; (f)–(h) the according variation of ρ_xx as a function of magnetic field under different carrier density n_1–3. A C = –2 state with ρ_yx = 0.5h/e² and ρ_xx = 0.05h/e² appears when magnetic field is increased to above 10 T for carrier density n₂. (a) and (b) are adopted from Ref. [58]. (c)–(h) are adopted from Ref. [111].

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图 10 磁场在MnBi₂Te₄陈绝缘体相中引起的C = 0的螺旋式拓扑态　(a)栅压在1—6 V之间时纵向电阻R_xx和霍尔电阻R_yx随磁场变化曲线, 栅压为4 V时, 30 T的磁场使C = –1陈绝缘体相被完全压制, 并引起一个以极宽零级霍尔平台为主要特征的C = 0态, 黑色虚线标注了零级平台出现位置时纵向电阻上的半整数量子化现象; (b)强磁场下塞曼效应引起的能带反转以及能带结构演化示意图; (c)在磁场引起的C = –1到C = 0拓扑相变过程中边缘态演化情况; (d)不同测量构型下的两端输运、三端输运以及非定域输运测量结果, 其中插图描述了不同的测量构型示意图, 玫红色虚线标记了由Landauer Büttiker公式预言的螺旋式边缘态贡献的量子化电阻数值. 图片来自文献[78]

Fig. 10. Magnetic field driven helical state with C = 0 in a MnBi₂Te₄ Chern insulator: (a) Magnetic field dependent longitudinal resistance R_xx and Hall resistance R_yx at 1 V ≤ V_g ≤ 6 V, at V_g = 4 V, the C = –1 state is completely suppressed when magnetic field is increased to above 30 T, followed by the C = 0 state characterized with a broad zero Hall plateau, the black dashed line denotes the half-quantized plateau of R_xx = 0.5h/e²; (b) schematic illustration of the electronic band structure evolution in strong magnetic field with Zeeman-effect-induced band inversion; (c) the evolution of edge states in the magnetic field driven topological phase transition between C = –1 and C = 0 phase; (d) two-, three-terminal, and nonlocal measurements in various configurations, the insets display the schematic layouts of the experimental setup, the expected quantized values for R_2T, R_3T, and R^NL derived from the Landauer Büttiker formalisms for helical edge transport are denoted by the broken magenta lines. The figures are adopted from Ref. [78].

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map

[1]	Klitzing K v, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[2]	Klitzing K v 1986 Rev. Mod. Phys. 58 519 Google Scholar
[3]	Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559 Google Scholar
[4]	Thouless D J, Kohmoto M, Nightingale M P, Dennijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[5]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[6]	Haldane F D M 2017 Rev. Mod. Phys. 89 040502 Google Scholar
[7]	Onoda M, Nagaosa N 2003 Phys. Rev. Lett. 90 206601 Google Scholar
[8]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[9]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[10]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[11]	Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802 Google Scholar
[12]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[13]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[14]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803 Google Scholar
[15]	Qi X L, Hughes T L, Zhang S C 2008 Phys. Rev. B 78 195424 Google Scholar
[16]	Niemi A J, Semenoff G W 1983 Phys. Rev. Lett. 51 2077 Google Scholar
[17]	Semenoff G W 1984 Phys. Rev. Lett. 53 2449 Google Scholar
[18]	Fradkin E, Dagotto E, Boyanovsky D 1986 Phys. Rev. Lett. 57 2967 Google Scholar
[19]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[20]	Nomura K, Nagaosa N 2011 Phys. Rev. Lett. 106 166802 Google Scholar
[21]	Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802 Google Scholar
[22]	Wilczek F 1987 Phys. Rev. Lett. 58 1799 Google Scholar
[23]	Li R D, Wang J, Qi X L, Zhang S C 2010 Nat. Phys. 6 284 Google Scholar
[24]	Qi X L, Witten E, Zhang S C 2013 Phys. Rev. B 87 134519
[25]	Wang J, Lian B, Zhang S C 2016 Phys. Rev. B 93 045115
[26]	Zirnstein H G, Rosenow B 2017 Phys. Rev. B 96 201112(R
[27]	Wang J, Lian B, Qi X L, Zhang S C 2015 Phys. Rev. B 92 081107 Google Scholar
[28]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
[29]	Zhou Z H, Chien Y J, Uher C 2006 Phys. Rev. B 74 224418 Google Scholar
[30]	Hor Y S, Roushan P, Beidenkopf H, Seo J, Qu D, Checkelsky J G, Wray L A, Hsieh D, Xia Y, Xu S Y, Qian D, Hasan M Z, Ong N P, Yazdani A, Cava R J 2010 Phys. Rev. B 81 195203 Google Scholar
[31]	Checkelsky J G, Ye J T, Onose Y, Iwasa Y, Tokura Y 2012 Nat. Phys. 8 729 Google Scholar
[32]	Zhang D M, Richardella A, Rench D W, Xu S Y, Kandala A, Flanagan T C, Beidenkopf H, Yeats A L, Buckley B B, Klimov P V, Awschalom D D, Yazdani A, Schiffer P, Hasan M Z, Samarth N 2012 Phys. Rev. B 86 205127 Google Scholar
[33]	Chang C Z, Zhang J S, Liu M H, Zhang Z C, Feng X, Li K, Wang L L, Chen X, Dai X, Fang Z, Qi X L, Zhang S C, Wang Y Y, He K, Ma X C, Xue Q K 2013 Adv. Mater. 25 1065 Google Scholar
[34]	Kou X F, Lang M R, Fan Y B, Jiang Y, Nie T X, Zhang J M, Jiang W J, Wang Y Y, Yao Y G, He L, Wang K L 2013 Acs Nano 7 9205 Google Scholar
[35]	Chang C Z, Zhang J S, Feng X, Shen J, Zhang Z C, Guo M H, Li K, Ou Y B, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S H, Chen X, Jia J F, Dai X, Fang Z, Zhang S C, He K, Wang Y Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[36]	Checkelsky J G, Yoshimi R, Tsukazaki A, Takahashi K S, Kozuka Y, Falson J, Kawasaki M, Tokura Y 2014 Nat. Phys. 10 731 Google Scholar
[37]	Kou X, Guo S T, Fan Y, Pan L, Lang M, Jiang Y, Shao Q, Nie T, Murata K, Tang J, Wang Y Y, He L, Lee T K, Lee W L, Wang K L 2014 Phys. Rev. Lett. 113 137201 Google Scholar
[38]	Chang C Z, Zhao W, Kim D Y, Zhang H, Assaf B A, Heiman D, Zhang S C, Liu C, Chan M H, Moodera J S 2015 Nat. Mater. 14 473 Google Scholar
[39]	Mogi M, Yoshimi R, Tsukazaki A, Yasuda K, Kozuka Y, Takahashi K S, Kawasaki M, Tokura Y 2015 Appl. Phys. Lett. 107 182401
[40]	Ou Y B, Liu C, Jiang G Y, Feng Y, Zhao D Y, Wu W X, Wang X X, Li W, Song C L, Wang L L, Wang W B, Wu W D, Wang Y Y, He K, Ma X C, Xue Q K 2018 Adv. Mater. 30 1703062 Google Scholar
[41]	Lee I, Kim C K, Lee J, Billinge S J L, Zhong R D, Schneeloch J A, Liu T S, Valla T, Tranquada J M, Gu G D, Davis J C S 2015 Proc. Natl. Acad. Sci. U. S. A. 112 1316 Google Scholar
[42]	Lachman E O, Young A F, Richardella A, et al. 2015 Sci. Adv. 1 e1500740 Google Scholar
[43]	Wang W B, Ou Y B, Liu C, Wang Y Y, He K, Xue Q K, Wu W D 2018 Nat. Phys. 14 791 Google Scholar
[44]	Yue Z, Raikh M E 2016 Phys. Rev. B 94 155313 Google Scholar
[45]	Xing Y X, Xu F M, Cheung K T, Sun Q F, Wang J, Yao Y G 2018 New J. Phys. 20 043011 Google Scholar
[46]	Chen C Z, Liu H, Xie X C 2019 Phys. Rev. Lett. 122 026601 Google Scholar
[47]	Haim A, Ilan R, Alicea J 2019 Phys. Rev. Lett. 123 046801 Google Scholar
[48]	Kudla S, Dyrdal A, Dugaev V K, Berakdar J, Barnas J 2019 Phys. Rev. B 100 205428 Google Scholar
[49]	Otrokov M M, Menshchikova T V, Rusinov I P, Vergniory M G, Kuznetsov V M, Chulkov E V 2017 Jetp. Lett. 105 297 Google Scholar
[50]	Otrokov M M, Menshchikova T V, Vergniory M G, Rusinov I P, Vyazovskaya A Y, Koroteev Y M, Bihlmayer G, Ernst A, Echenique P M, Arnau A, Chulkov E V 2017 2D Mater 4 025082 Google Scholar
[51]	Gong Y, Guo J W, Li J H, et al. 2019 Chin. Phys. Lett. 36 076801 Google Scholar
[52]	Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, Xu Y 2019 Sci. Adv. 5 eaaw5685 Google Scholar
[53]	Otrokov M M, Klimovskikh I I, Bentmann H, et al. 2019 Nature 576 416 Google Scholar
[54]	Rienks E D L, Wimmer S, Sanchez-Barriga J, Caha O, Mandal P S, Ruzicka J, Ney A, Steiner H, Volobuev V V, Groiss H, Albu M, Kothleitner G, Michalicka J, Khan S A, Minar J, Ebert H, Bauer G, Freyse F, Varykhalov A, Rader O, Springholz G 2019 Nature 576 423 Google Scholar
[55]	Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401 Google Scholar
[56]	Deng Y, Yu Y, Shi M Z, Guo Z, Xu Z, Wang J, Chen X H, Zhang Y 2020 Science 367 895 Google Scholar
[57]	Liu C, Wang Y C, Li H, Wu Y, Li Y X, Li J H, He K, Xu Y, Zhang J S, Wang Y Y 2020 Nat. Mater. 19 522 Google Scholar
[58]	Ge J, Liu Y, Li J, Li H, Luo T, Wu Y, Xu Y, Wang J 2020 Natl. Sci. Rev. 7 1280 Google Scholar
[59]	Zhang R X, Wu F, Sarma S D 2020 Phys. Rev. Lett. 124 136407 Google Scholar
[60]	Zhang J, Liu Z, Wang J 2019 Phys. Rev. B 100 165117 Google Scholar
[61]	Li J, Wang C, Zhang Z, Gu B L, Duan W, Xu Y 2019 Phys. Rev. B 100 121103 Google Scholar
[62]	Bestwick A J, Fox E J, Kou X, Pan L, Wang K L, Goldhaber-Gordon D 2015 Phys. Rev. Lett. 114 187201 Google Scholar
[63]	Chang C Z, Zhao W, Kim D Y, Wei P, Jain J K, Liu C, Chan M H, Moodera J S 2015 Phys. Rev. Lett. 115 057206 Google Scholar
[64]	Feng Y, Feng X, Ou Y, Wang J, Liu C, Zhang L, Zhao D, Jiang G, Zhang S C, He K, Ma X, Xue Q K, Wang Y Y 2015 Phys. Rev. Lett. 115 126801 Google Scholar
[65]	Liu M, Wang W, Richardella A R, Kandala A, Li J, Yazdani A, Samarth N, Ong N P 2016 Sci. Adv. 2 e1600167 Google Scholar
[66]	Feng X, Feng Y, Wang J, Ou Y B, Hao Z Q, Liu C, Zhang Z C, Zhang L G, Lin C J, Liao J, Li Y Q, Wang L L, Ji S H, Chen X, Ma X C, Zhang S C, Wang Y Y, He K, Xue Q K 2016 Adv. Mater. 28 6386 Google Scholar
[67]	Chang C Z, Zhao W, Li J, Jain J K, Liu C, Moodera J S, Chan M H 2016 Phys. Rev. Lett. 117 126802 Google Scholar
[68]	Yasuda K, Wakatsuki R, Morimoto T, Yoshimi R, Tsukazaki A, Takahashi K S, Ezawa M, Kawasaki M, Nagaosa N, Tokura Y 2016 Nat. Phys. 12 555 Google Scholar
[69]	Liu C, Zang Y Y, Ruan W, Gong Y, He K, Ma X C, Xue Q K, Wang Y Y 2017 Phys. Rev. Lett. 119 176809 Google Scholar
[70]	Mogi M, Kawamura M, Tsukazaki A, Yoshimi R, Takahashi K S, Kawasaki M, Tokura Y 2017 Sci. Adv. 3 eaao1669 Google Scholar
[71]	Mogi M, Kawamura M, Yoshimi R, Tsukazaki A, Kozuka Y, Shirakawa N, Takahashi K S, Kawasaki M, Tokura Y 2017 Nat. Mater. 16 516 Google Scholar
[72]	Xiao D, Jiang J, Shin J H, Wang W, Wang F, Zhao Y F, Liu C, Wu W, Chan M H W, Samarth N, Chang C Z 2018 Phys. Rev. Lett. 120 056801 Google Scholar
[73]	Watanabe R, Yoshimi R, Kawamura M, Mogi M, Tsukazaki A, Yu X Z, Nakajima K, Takahashi K S, Kawasaki M, Tokura Y 2019 Appl. Phys. Lett. 115 102403 Google Scholar
[74]	Otrokov M M, Rusinov I P, Blanco-Rey M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, Chulkov E V 2019 Phys. Rev. Lett. 122 107202 Google Scholar
[75]	Yan J Q, Zhang Q, Heitmann T, Huang Z, Chen K Y, Cheng J G, Wu W, Vaknin D, Sales B C, McQueeney R J 2019 Phys. Rev. Mater. 3 064202 Google Scholar
[76]	Zhang S, Wang R, Wang X, Wei B, Chen B, Wang H, Shi G, Wang F, Jia B, Ouyang Y, Xie F, Fei F, Zhang M, Wang X, Wu D, Wan X, Song F, Zhang H, Wang B 2020 Nano Lett. 20 709 Google Scholar
[77]	Liu C, Ou Y B, Feng Y, Jiang G Y, Wu W X, Li S R, Cheng Z J, He K, Ma X C, Xue Q K, Wang Y Y 2020 Phys. Rev. X 10 041063
[78]	Liu C, Wang Y C, Yang M, Mao J H, Li H, Li Y X, Li J H, Zhu H P, Wang J F, Li L, Wu Y, Xu Y, Zhang J S, Wang Y Y 2021 Nat. Commun. 12 4647 Google Scholar
[79]	Qiu J X, Tzschaschel C, Ahn J, Gao A, Li H, Zhang X Y, Ghosh B, Hu C, Wang Y X, Liu Y F, Berube D, Dinh T, Gong Z, Lien S W, Ho S C, Singh B, Watanabe K, Taniguchi T, Bell D C, Lu H Z, Bansil A, Lin H, Chang T R, Zhou B B, Ma Q, Vishwanath A, Ni N, Xu S Y 2023 Nat. Mater. 22 583 Google Scholar
[80]	Okazaki Y, Oe T, Kawamura M, Yoshimi R, Nakamura S, Takada S, Mogi M, Takahashi K S, Tsukazaki A, Kawasaki M, Tokura Y, Kaneko N H 2022 Nat. Phys. 18 25 Google Scholar
[81]	Gao A, Liu Y F, Hu C, Qiu J X, et al. 2021 Nature 595 521 Google Scholar
[82]	Mogi M, Okamura Y, Kawamura M, Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Morimoto T, Nagaosa N, Kawasaki M, Takahashi Y, Tokura Y 2022 Nat. Phys. 18 390 Google Scholar
[83]	Chen Y L, Analytis J G, Chu J H, Liu Z K, Mo S K, Qi X L, Zhang H J, Lu D H, Dai X, Fang Z, Zhang S C, Fisher I R, Hussain Z, Shen Z X 2009 Science 325 178 Google Scholar
[84]	Zhang Y, He K, Chang C Z, Song C L, Wang L L, Chen X, Jia J F, Fang Z, Dai X, Shan W Y, Shen S Q, Niu Q, Qi X L, Zhang S C, Ma X C, Xue Q K 2010 Nat. Phys. 6 584 Google Scholar
[85]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[86]	Zhang J S, Chang C Z, Zhang Z C, Wen J, Feng X, Li K, Liu M H, He K, Wang L L, Chen X, Xue Q K, Ma X C, Wang Y Y 2011 Nat. Commun. 2 574 Google Scholar
[87]	Liu Q, Liu C X, Xu C, Qi X L, Zhang S C 2009 Phys. Rev. Lett. 102 156603 Google Scholar
[88]	Sessi P, Reis F, Bathon T, Kokh K A, Tereshchenko O E, Bode M 2014 Nat. Commun. 5 5349 Google Scholar
[89]	Li M D, Chang C Z, Wu L J, Tao J, Zhao W W, Chan M H W, Moodera J S, Li J, Zhu Y M 2015 Phys. Rev. Lett. 114 146802 Google Scholar
[90]	Jiang J, Xiao D, Wang F, Shin J H, Andreoli D, Zhang J, Xiao R, Zhao Y F, Kayyalha M, Zhang L, Wang K, Zang J, Liu C, Samarth N, Chan M H W, Chang C Z 2020 Nat. Mater. 19 732 Google Scholar
[91]	Dziom V, Shuvaev A, Pimenov A, Astakhov G V, Ames C, Bendias K, Bottcher J, Tkachov G, Hankiewicz E M, Brune C, Buhmann H, Molenkamp L W 2017 Nat. Commun. 8 15197 Google Scholar
[92]	Okada K N, Takahashi Y, Mogi M, Yoshimi R, Tsukazaki A, Takahashi K S, Ogawa N, Kawasaki M, Tokura Y 2016 Nat. Commun. 7 12245 Google Scholar
[93]	Wu L, Salehi M, Koirala N, Moon J, Oh S, Armitage N P 2016 Science 354 1124 Google Scholar
[94]	He Q L, Hughes T L, Armitage N P, Tokura Y, Wang K L 2022 Nat. Mater. 21 15 Google Scholar
[95]	Mellnik A R, Lee J S, Richardella A, Grab J L, Mintun P J, Fischer M H, Vaezi A, Manchon A, Kim E A, Samarth N, Ralph D C 2014 Nature 511 449 Google Scholar
[96]	Kondou K, Yoshimi R, Tsukazaki A, Fukuma Y, Matsuno J, Takahashi K S, Kawasaki M, Tokura Y, Otani Y 2016 Nat. Phys. 12 1027 Google Scholar
[97]	Li C H, van 't Erve O M J, Robinson J T, Liu Y, Li L, Jonker B T 2014 Nat. Nanotechnol. 9 218 Google Scholar
[98]	Gotz M, Fijalkowski K M, Pesel E, Hartl M, Schreyeck S, Winnerlein M, Grauer S, Scherer H, Brunner K, Gould C, Ahlers F J, Molenkamp L W 2018 Appl. Phys. Lett. 112 072102 Google Scholar
[99]	Okazaki Y, Oe T, Kawamura M, Yoshimi R, Nakamura S, Takada S, Mogi M, Takahashi K S, Tsukazaki A, Kawasaki M, Tokura Y, Kaneko N H 2020 Appl. Phys. Lett. 116 143101
[100]	Fox E J, Rosen I T, Yang Y F, Jones G R, Elmquist R E, Kou X F, Pan L, Wang K L, Goldhaber-Gordon D 2018 Phys. Rev. B 98 075145 Google Scholar
[101]	Lee D S, Kim T H, Park C H, Chung C Y, Lim Y S, Seo W S, Park H H 2013 Crystengcomm 15 5532 Google Scholar
[102]	Sun H Y, Xia B W, Chen Z J, Zhang Y J, Liu P F, Yao Q S, Tang H, Zhao Y J, Xu H, Liu Q H 2019 Phys. Rev. Lett. 123 096401 Google Scholar
[103]	Wu J Z, Liu F C, Sasase M, Ienaga K, Obata Y, Yukawa R, Horiba K, Kumigashira H, Okuma S, Inoshita T, Hosono H 2019 Sci. Adv. 5 eaax9989 Google Scholar
[104]	Chen B, Fei F C, Zhang D Q, et al. 2019 Nat. Commun. 10 4469 Google Scholar
[105]	Li H, Gao S Y, Duan S F, et al. 2019 Phys. Rev. X 9 041039
[106]	Hao Y J, Liu P F, Feng Y, et al. 2019 Phys. Rev. X 9 041038
[107]	Chen Y J, Xu L X, Li J H, Li Y W, Zhang C F, Li H, Wu Y, Liang A J, Chen C, Jung S W, Cacho C, Wang H Y, Mao Y H, Liu S, Wang M X, Guo Y F, Xu Y, Liu Z K, Yang L X, Chen Y L 2019 Phys. Rev. X 9 041040
[108]	Swatek P, Wu Y, Wang L L, Lee K, Schrunk B, Yan J Q, Kaminski A 2020 Phys. Rev. B 101 161109 Google Scholar
[109]	Nevola D, Li H X, Yan J Q, Moore R G, Lee H N, Miao H, Johnson P D 2020 Phys. Rev. Lett. 125 117205 Google Scholar
[110]	Ovchinnikov D, Huang X, Lin Z, Fei Z Y, Cai J Q, Song T C, He M H, Jiang Q N, Wang C, Li H, Wang Y Y, Wu Y, Xiao D, Chu J H, Yan J Q, Chang C Z, Cui Y T, Xu X D 2021 Nano Lett. 21 2544 Google Scholar
[111]	Cai J Q, Ovchinnikov D, Fei Z Y, He M H, Song T C, Lin Z, Wang C, Cobden D, Chu J H, Cui Y T, Chang C Z, Xiao D, Yan J Q, Xu X D 2022 Nat. Commun. 13 1668 Google Scholar
[112]	Ying Z, Zhang S, Chen B, Jia B, Fei F, Zhang M, Zhang H, Wang X, Song F 2022 Phys. Rev. B 105 085412 Google Scholar
[113]	Yang S Q, Xu X L, Zhu Y Z, Niu R R, Xu C Q, Peng Y X, Cheng X, Jia X H, Huang Y, Xu X F, Lu J M, Ye Y 2021 Phys. Rev. X 11 011003
[114]	Cui J H, Shi M Z, Wang H H, Yu F H, Wu T, Luo X G, Ying J J, Chen X H 2019 Phys. Rev. B 99 155125 Google Scholar
[115]	Li H, Liu S, Liu C, Zhang J, Xu Y, Yu R, Wu Y, Zhang Y, Fan S 2020 Phys. Chem. Chem. Phys. 22 556 Google Scholar
[116]	Yan J-Q, Huang Z, Wu W, May A F 2022 J. Alloy Compd. 906 164327 Google Scholar
[117]	Hu C, Gao A, Berggren B S, Li H, Kurleto R, Narayan D, Zeljkovic I, Dessau D, Xu S, Ni N 2021 Phys. Rev. Mater. 5 124206 Google Scholar
[118]	Zhang J S, Chang C Z, Tang P Z, Zhang Z C, Feng X, Li K, Wang L L, Chen X, Liu C, Duan W, He K, Xue Q K, Ma X, Wang Y 2013 Science 339 1582 Google Scholar
[119]	Li B, Yan J Q, Pajerowski D M, Gordon E, Nedic A M, Sizyuk Y, Ke L Q, Orth P P, Vaknin D, McQueeney R J 2020 Phys. Rev. Lett. 124 167204 Google Scholar
[120]	Sass P M, Kim J, Vanderbilt D, Yan J Q, Wu W D 2020 Phys. Rev. Lett. 125 037201 Google Scholar
[121]	Sass P M, Ge W B, Yan J Q, Obeysekera D, Yang J J, Wu W D 2020 Nano Lett 20 2609 Google Scholar
[122]	Lai Y, Ke L Q, Yan J Q, McDonald R D, McQueeney R J 2021 Phys. Rev. B 103 184429 Google Scholar
[123]	Estyunin D A, Klimovskikh I I, Shikin A M, Schwier E F, Otrokov M M, Kimura A, Kumar S, Filnov S O, Aliev Z S, Babanly M B, Chulkov E V 2020 APL Mater 8 021105 Google Scholar
[124]	Li Y, Liu C, Wang Y, Lian Z, Li H, Wu Y, Zhang J, Wang Y 2023 Science Bulletin 68 1252
[125]	Shikin A M, Estyunin D A, Zaitsev N L, et al. 2021 Phys. Rev. B 104 115168 Google Scholar
[126]	Tan H, Yan B 2023 Phys. Rev. Lett. 130 126702 Google Scholar
[127]	Kivelson S, Lee D H, Zhang S C 1992 Phys. Rev. B 46 2223 Google Scholar
[128]	Hilke M, Shahar D, Song S H, Tsui D C, Xie Y H, Monroe D 1998 Nature 395 675 Google Scholar
[129]	Wong L W, Jiang H W, Trivedi N, Palm E 1995 Phys. Rev. B 51 18033 Google Scholar
[130]	Shahar D, Tsui D C, Shayegan M, Bhatt R N, Cunningham J E 1995 Phys. Rev. Lett. 74 4511 Google Scholar
[131]	Pan W, Shahar D, Tsui D C, Wei H P, Razeghi M 1997 Phys. Rev. B 55 15431 Google Scholar
[132]	Kou X F, Pan L, Wang J, Fan Y B, Choi E S, Lee W L, Nie T X, Murata K, Shao Q M, Zhang S C, Wang K L 2015 Nat. Commun. 6 8474 Google Scholar
[133]	Kawamura M, Mogi M, Yoshimi R, Tsukazaki A, Kozuka Y, Takahashi K S, Kawasaki M, Tokura Y 2018 Phys. Rev. B 98 140404(R
[134]	Wu X Y, Xiao D, Chen C Z, Sun J, Zhang L, Chan M H W, Samarth N, Xie X C, Lin X, Chang C Z 2020 Nat. Commun. 11 4532 Google Scholar
[135]	Kayyalha M, Xiao D, Zhang R X, Shin J, Jiang J, Wang F, Zhao Y F, Xiao R, Zhang L, Fijalkowski K M, Mandal P, Winnerlein M, Gould C, Li Q, Molenkamp L W, Chan M H W, Samarth N, Chang C Z 2020 Science 367 64 Google Scholar
[136]	Huang Y Y, Setiawan F, Sau J D 2018 Phys. Rev. B 97 100501(R
[137]	Ji W J, Wen X G 2018 Phys. Rev. Lett. 120 107002 Google Scholar
[138]	Wang J, Zhou Q, Lian B A, Zhang S C 2015 Phys. Rev. B 92 064520 Google Scholar
[139]	Lian B A, Wang J, Sun X Q, Vaezi A, Zhang S C 2018 Phys. Rev. B 97 125408 Google Scholar
[140]	Lian B, Sun X Q, Vaezi A, Qi X L, Zhang S C 2018 Proc. Natl. Acad. Sci. U. S. A. 115 10938 Google Scholar
[141]	Liu C, Zang Y Y, Gong Y, He K, Ma X C, Xue Q K, Wang Y Y 2022 Sci. China Phys. Mech. 65 266812 Google Scholar
[142]	Zhu J J, Yao D X, Zhang S C, Chang K 2011 Phys. Rev. Lett. 106 097201 Google Scholar
[143]	Xu Z M, Duan W H, Xu Y 2022 Nano Lett. 23 305
[144]	Li Y X, Liu C, Wang Y C, Li H, Wu Y, Zhang J S, Wang Y Y 2022 J. Phys. D Appl. Phys. 55 104001 Google Scholar
[145]	Marsh D J E, Fong K C, Lentz E W, Smejkal L, Ali M N 2019 Phys. Rev. Lett. 123 121601 Google Scholar
[146]	Nenno D M, Garcia C A C, Gooth J, Felser C, Narang P 2020 Nat. Rev. Phys. 2 682 Google Scholar
[147]	Sekine A, Nomura K 2021 J. Appl. Phys. 129 141101 Google Scholar
[148]	Li H L, Chen C Z, Jiang H, Xie X C 2021 Phys. Rev. Lett. 127 236402 Google Scholar
[149]	Roth A, Brune C, Buhmann H, Molenkamp L W, Maciejko J, Qi X L, Zhang S C 2009 Science 325 294 Google Scholar
[150]	Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[151]	Young A F, Sanchez-Yamagishi J D, Hunt B, Choi S H, Watanabe K, Taniguchi T, Ashoori R C, Jarillo-Herrero P 2014 Nature 505 528 Google Scholar
[152]	Veyrat L, Déprez C, Coissard A, Li X, Gay F, Watanabe K, Taniguchi T, Han Z, Piot B A, Sellier H, Sacépé B 2020 Science 367 781 Google Scholar
[153]	Chen R, Li S, Sun H P, Liu Q H, Zhao Y, Lu H Z, Xie X C 2021 Phys. Rev. B 103 L241409 Google Scholar
[154]	Gu M Q, Li J Y, Sun H Y, Zhao Y F, Liu C, Liu J P, Lu H Z, Liu Q H 2021 Nat. Commun. 12 3524 Google Scholar
[155]	Zhou H M, Li H L, Xu D H, Chen C Z, Sun Q F, Xie X C 2022 Phys. Rev. Lett. 129 096601 Google Scholar
[156]	Gong M, Liu H W, Jiang H, Chen C Z, Xie X C 2023 Natl. Sci. Rev. 10 nwad025 Google Scholar
[157]	Zou J Y, Fu B, Wang H W, Hu Z A, Shen S Q 2022 Phys. Rev. B 105 L201106 Google Scholar
[158]	Sun S, Weng H M, Dai X 2022 Phys. Rev. B 106 L241105 Google Scholar
[159]	Song Z D, Lian B A, Queiroz R, Ilan R, Bernevig B A, Stern A 2021 Phys. Rev. Lett. 127 016602
[160]	Wang J, Lian B, Zhang S C 2014 Phys. Rev. B 89 085106 Google Scholar
[161]	Liang S, Kushwaha S, Gao T, Hirschberger M, Li J, Wang Z, Stolze K, Skinner B, Bernevig B A, Cava R J, Ong N P 2019 Nat. Mater. 18 443 Google Scholar
[162]	Bottcher J, Tutschku C, Hankiewicz E M 2020 Phys. Rev. B 101 195433 Google Scholar
[163]	Bottcher J, Tutschku C, Molenkamp L W, Hankiewicz E M 2019 Phys. Rev. Lett. 123 226602 Google Scholar
[164]	Lian B, Liu Z C, Zhang Y B, Wang J 2020 Phys. Rev. Lett. 124 126402

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磁性拓扑绝缘体中的量子输运现象