二维材料中贝里曲率诱导的磁性响应

刘雨亭; 贺文宇; 刘军伟; 邵启明

doi:10.7498/aps.70.20202132

摘要

二维材料中由贝里曲率诱导的新型磁学响应是近年来的新兴领域. 这些二维材料所表现出的磁学特性及量子输运与贝里曲率直接相关, 而贝里曲率又与晶体的对称性、电子的轨道磁性、自旋轨道耦合以及磁电效应等息息相关. 研究这些新型磁性响应一方面有益于研究不同量子效应间的耦合作用, 另一方面可探索量子效应在电子与信息器件领域的应用. 本文介绍了近几年来二维材料中新型磁响应的实验研究进展, 特别介绍了二硫化钼和石墨烯等材料中的谷霍尔和磁电效应、低对称性的二碲化钨等材料中的量子非线性霍尔以及转角石墨烯中的反常霍尔和量子反常霍尔效应. 本文结合二维材料的晶体结构以及电子结构, 介绍了这些新奇现象的现有物理解释、回顾了相关研究的最新发展、讨论了其中尚未理解的现象, 并作出展望.

关键词:

Abstract

The magnetic response in a two-dimensional material has received increasing attention in recent years. The magnetic effects and related quantum transport originate from Berry curvature, which is associated with crystal symmetry and many quantum effects including electrons’ orbital magnetism, spin-orbit coupling, and magnetoelectricity. The importance of studying the magnetic response in the two-dimensional material lies in two aspects. First, the magnetic response of two-dimensional material provides a platform to investigate the coupling between the above-mentioned intrinsic quantum effects and their couplings. Second, it possesses the potential applications in energy-efficient quantum and spintronic devices. Here, we review the experimental research progress made in recent years. In particular, we focus on the research progress of the valley Hall and magnetoelectric effect, quantum non-linear Hall effect, anomalous Hall, and quantum anomalous Hall effect in two-dimensional materials such as graphene, transition-metal chalcogenides, and twisted bilayer graphene. For each session, we first introduce these phenomena and their underlying physics by using crystal symmetries and band structures. Then, we summarize the experimental results and identify unsolved problems. At last, we provide an outlook in this emerging research direction.

Keywords:

作者及机构信息

1.
香港科技大学电子与计算机工程系, 香港　999077

2.
香港科技大学物理系, 香港　999077

通信作者: 邵启明, eeqshao@ust.hk

基金项目: 香港研究资助局 (批准号: ECS26200520, N_HKUST626/18, 26302118, 16305019)、香港科技大学启动经费和博士后匹配基金(批准号: NA389)资助的课题

Authors and contacts

1.
Department of Electronic and Computing Engineering, The Hong Kong University of Science and Technology, Hong Kong 999077, China

2.
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong 999077, China

Corresponding author: Shao Qi-Ming, eeqshao@ust.hk

Funds: Project supported by the HK University Grant Committee (Grant Nos. ECS26200520, N_HKUST626/18, 26302118, 16305019), the HKUST ECE Start-up Fund, and the HKUST Postdoctoral Fellowship Matching Fund (Grant No. NA389)

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参考文献

[1]	Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605 Google Scholar
[2]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[3]	Zhang Y H, Mao D, Senthil T 2019 Phys. Rev. Res. 1 033126 Google Scholar
[4]	Sjöstrand T J, Karlsson K, Aryasetiawan F 2019 Phys. Rev. B 100 054427 Google Scholar
[5]	Xiao D, Yao Y, Fang Z, Niu Q 2006 Phys. Rev. Lett. 97 026603 Google Scholar
[6]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[7]	Murakami S 2006 Phys. Rev. Lett. 97 236805 Google Scholar
[8]	Essin A M, Turner A M, Moore J E, Vanderbilt D 2010 Phys. Rev. B 81 205104 Google Scholar
[9]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[10]	Malashevich A, Souza I, Coh S, Vanderbilt D 2010 New J. Phys. 12 053032 Google Scholar
[11]	Xiao D, Shi J, Niu Q 2005 Phys. Rev. Lett. 95 137204 Google Scholar
[12]	Thonhauser T, Ceresoli D, Vanderbilt D, Resta R 2005 Phys. Rev. Lett. 95 137205 Google Scholar
[13]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[14]	Schaibley J R, Yu H, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 1
[15]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[16]	Saito R, Tatsumi Y, Huang S, Ling X, Dresselhaus M S 2016 J. Phys. Condens. Matter 28 353002 Google Scholar
[17]	Zhao S, Dong B, Wang H, Wang H, Zhang Y, Han Z V, Zhang H 2020 Nanoscale Adv. 2 109 Google Scholar
[18]	Qian X, Liu J, Fu L, Li J 2014 Science 346 1344 Google Scholar
[19]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[20]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[21]	Li L, Yang F, Ye G J, Zhang Z, Zhu Z, Lou W, Zhou X, Li L, Watanabe K, Taniguchi T, Chang K, Wang Y, Chen X H, Zhang Y 2016 Nat. Nanotechnol. 11 593 Google Scholar
[22]	Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76 Google Scholar
[23]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002 Google Scholar
[24]	Kim J, Jin C, Chen B, Cai H, Zhao T, Lee P, Kahn S, Watanabe K, Taniguchi T, Tongay S, Crommie M F, Wang F 2017 Sci. Adv. 3 e1700518 Google Scholar
[25]	Lee J, Wang Z, Xie H, Mak K F, Shan J 2017 Nat. Mater. 16 887 Google Scholar
[26]	Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N, Jarillo-Herrero P 2019 Nature 565 337 Google Scholar
[27]	Kang K, Li T, Sohn E, Shan J, Mak K F 2019 Nat. Mater. 18 324 Google Scholar
[28]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213
[29]	Fiebig M 2005 J. Phys. Appl. Phys. 38 R123 Google Scholar
[30]	Rycerz A, Tworzydło J, Beenakker C W J 2007 Nat. Phys. 3 172 Google Scholar
[31]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489 Google Scholar
[32]	Gorbachev R V, Song J C W, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448 Google Scholar
[33]	Sui M, Chen G, Ma L, Shan W Y, Tian D, Watanabe K, Taniguchi T, Jin X, Yao W, Xiao D, Zhang Y 2015 Nat. Phys. 11 1027 Google Scholar
[34]	Shimazaki Y, Yamamoto M, Borzenets I V, Watanabe K, Taniguchi T, Tarucha S 2015 Nat. Phys. 11 1032 Google Scholar
[35]	Lee J, Mak K F, Shan J 2016 Nat. Nanotechnol. 11 421 Google Scholar
[36]	Huang Z, Liu Y, Dini K, Tan Q, Liu Z, Fang H, Liu J, Liew T, Gao W 2020 Nano Lett. 20 1345 Google Scholar
[37]	Zhang Y J, Oka T, Suzuki R, Ye J T, Iwasa Y 2014 Science 344 725 Google Scholar
[38]	Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290 Google Scholar
[39]	Kim J, Hong X, Jin C, Shi S F, Chang C Y S, Chiu M H, Li L J, Wang F 2014 Science 346 1205 Google Scholar
[40]	Li Y, Ludwig J, Low T, Chernikov A, Cui X, Arefe G, Kim Y D, van der Zande A M, Rigosi A, Hill H M, Kim S H, Hone J, Li Z, Smirnov D, Heinz T F 2014 Phys. Rev. Lett. 113 266804 Google Scholar
[41]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[42]	Aivazian G, Gong Z, Jones A M, Chu R L, Yan J, Mandrus D G, Zhang C, Cobden D, Yao W, Xu X 2015 Nat. Phys. 11 148 Google Scholar
[43]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[44]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormányos A, Zólyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[45]	Ye Y, Xiao J, Wang H, Ye Z, Zhu H, Zhao M, Wang Y, Zhao J, Yin X, Zhang X 2016 Nat. Nanotechnol. 11 598 Google Scholar
[46]	Cracknell A P1975 Magnetism in Crystalline Materials (1st Ed.) (Oxford: Pergamon Press)
[47]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[48]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nanotechnol. 7 490 Google Scholar
[49]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[50]	Weng H, Yu R, Hu X, Dai X, Fang Z 2015 Adv. Phys. 64 227 Google Scholar
[51]	de Juan F, Grushin A G, Morimoto T, Moore J E 2017 Nat. Commun. 8 15995 Google Scholar
[52]	You J S, Fang S, Xu S Y, Kaxiras E, Low T 2018 Phys. Rev. B 98 121109R Google Scholar
[53]	Zhang Y, Brink J van den, Felser C, Yan B 2018 2D Mater. 5 044001
[54]	Shi L, Song J C W 2019 Phys. Rev. B 99 035403 Google Scholar
[55]	Tian Y, Li Y, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
[56]	Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, Deviatov E V 2019 JETP Lett. 109 715 Google Scholar
[57]	Huang M, Wu Z, Hu J, Cai X, Li E, An L, Feng X, Ye Z, Lin N, Law K T, Wang N 2020 arXiv: 2006.05615 [cond-mat.mes-hall]
[58]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji ZQ, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[59]	刘健鹏, 戴希 2020 69 147301 Google Scholar Liu J P, Dai X 2020 Acta Phys. Sin. 69 147301 Google Scholar
[60]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[61]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C and Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[62]	Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56 Google Scholar
[63]	Chen S, He M, Zhang Y H, Hsieh V, Fei Z, Watanabe K, Taniguchi T, Cobden D H, Xu X, Dean C R, Yankowitz M 2020 Nat. Phys. 17 374
[64]	Polshyn H, Zhu J, Kumar M A, Zhang Y, Yang F, Tschirhart C L, Serlin M, Watanabe K, Taniguchi T, MacDonald A H, Young A F 2020 Nature 588 66 Google Scholar
[65]	Zhu J, Su J J, MacDonald A H 2020 Phys. Rev. Lett. 125 227702 Google Scholar
[66]	Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 Google Scholar
[67]	Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059 Google Scholar
[68]	Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A, Pasupathy A N 2019 Nature 572 95 Google Scholar
[69]	Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y, Ren H, Alicea J, Refael G, von Oppen F, Watanabe K, Taniguchi T, Nadj-Perge S 2019 Nat. Phys. 15 1174 Google Scholar
[70]	Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[71]	Lee D S, Riedl C, Beringer T, Castro Neto A H, von Klitzing K, Starke U, Smet J H 2011 Phys. Rev. Lett. 107 216602 Google Scholar
[72]	Kim Y, Park J, Song I, Ok J M, Jo Y, Watanabe K, Taniquchi T, Choi H C, Lee D S, Jung S, Kim J S 2016 Sci. Rep. 6 38068 Google Scholar
[73]	Moon P, Koshino M 2012 Phys. Rev. B 85 195458 Google Scholar
[74]	He W Y, Goldhaber-Gordon D, Law K T 2020 Nat. Commun. 11 1650 Google Scholar
[75]	He W Y, Law K T 2020 Phys. Rev. Res. 2 012073 Google Scholar
[76]	Liu Y, Shao Q 2020 ACS Nano 14 9389 Google Scholar
[77]	Xie M, MacDonald A H 2020 Phys. Rev. Lett. 124 097601 Google Scholar
[78]	Bultinck N, Chatterjee S, Zaletel M P 2020 Phys. Rev. Lett. 124 166601 Google Scholar
[79]	Peng R, Ma Y, Xu X, He Z, Huang B, Dai Y 2020 Phys. Rev. B 102 035412 Google Scholar
[80]	Ma Y, Kou L, Du A, Huang B, Dai Y, Heine T 2018 Phys. Rev. B 97 035444 Google Scholar
[81]	Xu Z, Zhang Q, Shen Q, Cheng Y, Schwingenschlögl U, Huang W 2017 J. Mater. Chem. C 5 10427 Google Scholar
[82]	Fu L 2009 Phys. Rev. Lett. 103 266801 Google Scholar
[83]	Alpichshev Z, Analytis J G, Chu J H, Fisher I R, Chen Y L, Shen Z X, Fang A, Kapitulnik A 2010 Phys. Rev. Lett. 104 016401 Google Scholar
[84]	Hosur P 2011 Phys. Rev. B 83 035309 Google Scholar
[85]	Zheng Z, Ma Q, Bi Z, de la Barrera S, Liu M H, Mao N, Zhang Y, Kiper N, Watanabe K, Taniguchi T, Kong J, Tisdale W A, Ashoori R, Gedik N, Fu L, Xu S Y, Jarillo-Herrero P 2020 Nature 588 71 Google Scholar

施引文献

图 1 受应力的单层硫化钼谷磁电效应示意图　(a)谷霍尔效应^[22]; (b)谷磁电效应^[25]; (c)自旋极化引起的磁矩和谷磁电性引起的磁矩在外磁场下的磁光克尔响应; (d)磁光克尔响应与施加电流方向和应力方向的关系

Fig. 1. Sketch of the magnetoelectric effect in monolayer MoS₂: (a) Valley Hall effect^[22]; (b) valley magnetoelectricity^[25]; (c) comparison of magneto-optical Kerr response between spin polarizations induced magnetism and valley magnetization under external magnetic fields; (d) valley magnetization-induced Kerr rotation as a function of the azimuthal angle of current for zigzag and armchair monolayer MoS₂.

下载: 全尺寸图片幻灯片

图 2 碲化钨中量子非线性霍尔效应示意图　(a)线性和非线性霍尔电压随电流的变化^[47]; (b)碲化钨在不同方向上的晶体结构示意图; (c)纵向电压和非线性霍尔电压与电流施加方向的关系^[27]; (d)非线性霍尔电压与材料电导率的关系. 插图表示了非线性霍尔效应的两种来源: 贝里曲率和电子偏散射输运^[27]

Fig. 2. Illustration of the quantum nonlinear Hall effect: (a) Dependence of linear and non-linear Hall voltage on applied currents^[47]; (b) crystal structure of WTe₂; (c) angular dependence of longitudinal voltage and non-linear Hall voltage^[27]; (d) relationship between nonlinear Hall voltage and conductance. The inset shows two origins of nonlinear Hall voltage: Intrinsic Berry curvature and skew scattering^[27].

下载: 全尺寸图片幻灯片

图 3 转角双层石墨烯中量子反常霍尔效应示意图　(a)自旋磁化和轨道磁化中量子反常霍尔效应对比示意图; (b)转角双层石墨烯中自旋极化和能谷非极化的导带示意图; (c)转角双层石墨烯中自旋和能谷完全极化的导带示意图; (d)量子反常霍尔态下, 霍尔电阻和纵向电阻随磁场的变化关系, 插图表示材料的导电状态—边缘导电和体导电; (e)电流控制反常霍尔态下磁性翻转示意图

Fig. 3. Illustration of quantum anomalous Hall effect in twisted bilayer graphene (tBLG): (a) Sketch of quantum anomalous Hall effect in spin magnetization and orbital magnetization systems; (b) schematic of fully spin-polarized and but valley-unpolarized conduction bands in a moiré unit cell of tBLG; (c) schematic of fully spin-polarized and valley-polarized conduction bands in a moiré unit cell of tBLG; (d) longitudinal resistance and Hall resistance as a function of magnetic field in the quantum anomalous Hall state, and the insets show the bulk and edge conduction states of material; (e) current control of magnetization switching in the anomalous Hall state.

下载: 全尺寸图片幻灯片

map

[1]	Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605 Google Scholar
[2]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[3]	Zhang Y H, Mao D, Senthil T 2019 Phys. Rev. Res. 1 033126 Google Scholar
[4]	Sjöstrand T J, Karlsson K, Aryasetiawan F 2019 Phys. Rev. B 100 054427 Google Scholar
[5]	Xiao D, Yao Y, Fang Z, Niu Q 2006 Phys. Rev. Lett. 97 026603 Google Scholar
[6]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[7]	Murakami S 2006 Phys. Rev. Lett. 97 236805 Google Scholar
[8]	Essin A M, Turner A M, Moore J E, Vanderbilt D 2010 Phys. Rev. B 81 205104 Google Scholar
[9]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[10]	Malashevich A, Souza I, Coh S, Vanderbilt D 2010 New J. Phys. 12 053032 Google Scholar
[11]	Xiao D, Shi J, Niu Q 2005 Phys. Rev. Lett. 95 137204 Google Scholar
[12]	Thonhauser T, Ceresoli D, Vanderbilt D, Resta R 2005 Phys. Rev. Lett. 95 137205 Google Scholar
[13]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[14]	Schaibley J R, Yu H, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 1
[15]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[16]	Saito R, Tatsumi Y, Huang S, Ling X, Dresselhaus M S 2016 J. Phys. Condens. Matter 28 353002 Google Scholar
[17]	Zhao S, Dong B, Wang H, Wang H, Zhang Y, Han Z V, Zhang H 2020 Nanoscale Adv. 2 109 Google Scholar
[18]	Qian X, Liu J, Fu L, Li J 2014 Science 346 1344 Google Scholar
[19]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[20]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[21]	Li L, Yang F, Ye G J, Zhang Z, Zhu Z, Lou W, Zhou X, Li L, Watanabe K, Taniguchi T, Chang K, Wang Y, Chen X H, Zhang Y 2016 Nat. Nanotechnol. 11 593 Google Scholar
[22]	Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76 Google Scholar
[23]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002 Google Scholar
[24]	Kim J, Jin C, Chen B, Cai H, Zhao T, Lee P, Kahn S, Watanabe K, Taniguchi T, Tongay S, Crommie M F, Wang F 2017 Sci. Adv. 3 e1700518 Google Scholar
[25]	Lee J, Wang Z, Xie H, Mak K F, Shan J 2017 Nat. Mater. 16 887 Google Scholar
[26]	Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N, Jarillo-Herrero P 2019 Nature 565 337 Google Scholar
[27]	Kang K, Li T, Sohn E, Shan J, Mak K F 2019 Nat. Mater. 18 324 Google Scholar
[28]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213
[29]	Fiebig M 2005 J. Phys. Appl. Phys. 38 R123 Google Scholar
[30]	Rycerz A, Tworzydło J, Beenakker C W J 2007 Nat. Phys. 3 172 Google Scholar
[31]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489 Google Scholar
[32]	Gorbachev R V, Song J C W, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448 Google Scholar
[33]	Sui M, Chen G, Ma L, Shan W Y, Tian D, Watanabe K, Taniguchi T, Jin X, Yao W, Xiao D, Zhang Y 2015 Nat. Phys. 11 1027 Google Scholar
[34]	Shimazaki Y, Yamamoto M, Borzenets I V, Watanabe K, Taniguchi T, Tarucha S 2015 Nat. Phys. 11 1032 Google Scholar
[35]	Lee J, Mak K F, Shan J 2016 Nat. Nanotechnol. 11 421 Google Scholar
[36]	Huang Z, Liu Y, Dini K, Tan Q, Liu Z, Fang H, Liu J, Liew T, Gao W 2020 Nano Lett. 20 1345 Google Scholar
[37]	Zhang Y J, Oka T, Suzuki R, Ye J T, Iwasa Y 2014 Science 344 725 Google Scholar
[38]	Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290 Google Scholar
[39]	Kim J, Hong X, Jin C, Shi S F, Chang C Y S, Chiu M H, Li L J, Wang F 2014 Science 346 1205 Google Scholar
[40]	Li Y, Ludwig J, Low T, Chernikov A, Cui X, Arefe G, Kim Y D, van der Zande A M, Rigosi A, Hill H M, Kim S H, Hone J, Li Z, Smirnov D, Heinz T F 2014 Phys. Rev. Lett. 113 266804 Google Scholar
[41]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[42]	Aivazian G, Gong Z, Jones A M, Chu R L, Yan J, Mandrus D G, Zhang C, Cobden D, Yao W, Xu X 2015 Nat. Phys. 11 148 Google Scholar
[43]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[44]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormányos A, Zólyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[45]	Ye Y, Xiao J, Wang H, Ye Z, Zhu H, Zhao M, Wang Y, Zhao J, Yin X, Zhang X 2016 Nat. Nanotechnol. 11 598 Google Scholar
[46]	Cracknell A P1975 Magnetism in Crystalline Materials (1st Ed.) (Oxford: Pergamon Press)
[47]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[48]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nanotechnol. 7 490 Google Scholar
[49]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[50]	Weng H, Yu R, Hu X, Dai X, Fang Z 2015 Adv. Phys. 64 227 Google Scholar
[51]	de Juan F, Grushin A G, Morimoto T, Moore J E 2017 Nat. Commun. 8 15995 Google Scholar
[52]	You J S, Fang S, Xu S Y, Kaxiras E, Low T 2018 Phys. Rev. B 98 121109R Google Scholar
[53]	Zhang Y, Brink J van den, Felser C, Yan B 2018 2D Mater. 5 044001
[54]	Shi L, Song J C W 2019 Phys. Rev. B 99 035403 Google Scholar
[55]	Tian Y, Li Y, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
[56]	Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, Deviatov E V 2019 JETP Lett. 109 715 Google Scholar
[57]	Huang M, Wu Z, Hu J, Cai X, Li E, An L, Feng X, Ye Z, Lin N, Law K T, Wang N 2020 arXiv: 2006.05615 [cond-mat.mes-hall]
[58]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji ZQ, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[59]	刘健鹏, 戴希 2020 69 147301 Google Scholar Liu J P, Dai X 2020 Acta Phys. Sin. 69 147301 Google Scholar
[60]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[61]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C and Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[62]	Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56 Google Scholar
[63]	Chen S, He M, Zhang Y H, Hsieh V, Fei Z, Watanabe K, Taniguchi T, Cobden D H, Xu X, Dean C R, Yankowitz M 2020 Nat. Phys. 17 374
[64]	Polshyn H, Zhu J, Kumar M A, Zhang Y, Yang F, Tschirhart C L, Serlin M, Watanabe K, Taniguchi T, MacDonald A H, Young A F 2020 Nature 588 66 Google Scholar
[65]	Zhu J, Su J J, MacDonald A H 2020 Phys. Rev. Lett. 125 227702 Google Scholar
[66]	Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 Google Scholar
[67]	Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059 Google Scholar
[68]	Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A, Pasupathy A N 2019 Nature 572 95 Google Scholar
[69]	Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y, Ren H, Alicea J, Refael G, von Oppen F, Watanabe K, Taniguchi T, Nadj-Perge S 2019 Nat. Phys. 15 1174 Google Scholar
[70]	Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[71]	Lee D S, Riedl C, Beringer T, Castro Neto A H, von Klitzing K, Starke U, Smet J H 2011 Phys. Rev. Lett. 107 216602 Google Scholar
[72]	Kim Y, Park J, Song I, Ok J M, Jo Y, Watanabe K, Taniquchi T, Choi H C, Lee D S, Jung S, Kim J S 2016 Sci. Rep. 6 38068 Google Scholar
[73]	Moon P, Koshino M 2012 Phys. Rev. B 85 195458 Google Scholar
[74]	He W Y, Goldhaber-Gordon D, Law K T 2020 Nat. Commun. 11 1650 Google Scholar
[75]	He W Y, Law K T 2020 Phys. Rev. Res. 2 012073 Google Scholar
[76]	Liu Y, Shao Q 2020 ACS Nano 14 9389 Google Scholar
[77]	Xie M, MacDonald A H 2020 Phys. Rev. Lett. 124 097601 Google Scholar
[78]	Bultinck N, Chatterjee S, Zaletel M P 2020 Phys. Rev. Lett. 124 166601 Google Scholar
[79]	Peng R, Ma Y, Xu X, He Z, Huang B, Dai Y 2020 Phys. Rev. B 102 035412 Google Scholar
[80]	Ma Y, Kou L, Du A, Huang B, Dai Y, Heine T 2018 Phys. Rev. B 97 035444 Google Scholar
[81]	Xu Z, Zhang Q, Shen Q, Cheng Y, Schwingenschlögl U, Huang W 2017 J. Mater. Chem. C 5 10427 Google Scholar
[82]	Fu L 2009 Phys. Rev. Lett. 103 266801 Google Scholar
[83]	Alpichshev Z, Analytis J G, Chu J H, Fisher I R, Chen Y L, Shen Z X, Fang A, Kapitulnik A 2010 Phys. Rev. Lett. 104 016401 Google Scholar
[84]	Hosur P 2011 Phys. Rev. B 83 035309 Google Scholar
[85]	Zheng Z, Ma Q, Bi Z, de la Barrera S, Liu M H, Mao N, Zhang Y, Kiper N, Watanabe K, Taniguchi T, Kong J, Tisdale W A, Ashoori R, Gedik N, Fu L, Xu S Y, Jarillo-Herrero P 2020 Nature 588 71 Google Scholar

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