磁场中拓扑物态的量子输运

强晓斌; 卢海舟

doi:10.7498/aps.70.20200914

摘要

拓扑物态包括拓扑绝缘体、拓扑半金属以及拓扑超导体. 拓扑物态奇异的能带结构以及受拓扑保护的新奇表面态, 使其具有了独特的输运性质. 拓扑半金属作为物质的一种三维拓扑态具有无能隙的准粒子激发, 根据导带和价带的接触类型分为外尔半金属、狄拉克半金属和节线半金属. 本文以拓扑半金属为主回顾了在磁场下拓扑物态中量子输运的最新工作, 在不同的磁场范围内分别给出了描述拓扑物态输运行为的主要理论.

关键词:

Topological matters include topological insulator, topological semimetal and topological superconductor. The topological semimetals are three-dimensional topological states of matter with gapless electronic excitations. They are simply divided into Weyl, Dirac, and nodal-line semimetals according to the touch type of the conduction band and the valence band. Their characteristic electronic structures lead to topologically protected surface states at certain surfaces, corresponding to the novel transport properties. We review our recent works on quantum transport mainly in topological semimetals. The main theories describing the transport behavior of topological matters are given in different magnetic regions.

Keywords:

作者及机构信息

强晓斌^1,2,
卢海舟^1,2

1.
南方科技大学物理系, 深圳量子科学与工程研究院, 深圳　518055

2.
深圳市量子科学与工程重点实验室, 深圳　518055

通信作者: 卢海舟, luhz@sustech.edu.cn

作者简介:

卢海舟, 2007年在清华大学高等研究院获博士学位. 同年赴香港大学做博士后研究, 2012年晋升为研究助理教授. 2015年加入南方科技大学, 现为物理系和深圳量子科学与工程研究院教授. 主要从事凝聚态物理, 特别是量子输运理论的研究. 研究兴趣集中在利用量子场论方法研究拓扑和新奇材料中的量子态和量子输运. 系统地研究了二维和三维狄拉克电子的量子输运行为, 并应用于拓扑绝缘体/半金属/超导体, 二维层状材料等. 研究过的物理效应包括弱局域化、奇异负磁阻、量子振荡、强磁场量子极限、各类霍尔效应等, 在拓扑半金属中提出了三维量子霍尔效应的一种基于费米弧的新机制, 多个理论工作被实验广泛支持和应用

基金项目: 国家重点基础研究发展计划(批准号: 2016YFA0301700)、国家自然科学基金(批准号: 11925402)、广东省自然科学基金(批准号: 2016ZT06D348)和深圳市科学技术创新委员会(批准号: ZDSYS20170303165926217, JCYJ20170412152620376)资助的课题

Authors and contacts

1.
Shenzhen Institute for Quantum Science and Engineering, Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China

2.
Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China

Corresponding author: Lu Hai-Zhou, luhz@sustech.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2016YFA0301700), the National Natural Science Foundation of China (Grant No. 11925402), the Natural Science Foundation of Guangdong Province, China (Grant No. 2016ZT06D348), and the Science and Technology Innovation Commission of Shenzhen, China (Grant Nos. ZDSYS20170303165926217, JCYJ20170412152620376)

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参考文献

[1]	Balents L 2011 Physics 4 36 Google Scholar
[2]	Volovik G E 2003 The Universe in a Helium Droplet (Vol. 117) (New York: Oxford University Press) pp32−41
[3]	Wan X, Turner A M, Vishwanath A, Savrasov S Y 2011 Phys. Rev. B 83 205101 Google Scholar
[4]	Yang K Y, Lu Y M, Ran Y 2011 Phys. Rev. B 84 075129 Google Scholar
[5]	Burkov A, Balents L 2011 Phys. Rev. Lett. 107 127205 Google Scholar
[6]	Xu G, Weng H, Wang Z, Dai X, Fang Z 2011 Phys. Rev. Lett. 107 186806 Google Scholar
[7]	Jiang J H 2012 Phys. Rev. A 85 033640 Google Scholar
[8]	Young S M, Zaheer S, Teo J C, Kane C L, Mele E J, Rappe A M 2012 Phys. Rev. Lett. 108 140405 Google Scholar
[9]	Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X, Fang Z 2012 Phys. Rev. B 85 195320 Google Scholar
[10]	Singh B, Sharma A, Lin H, Hasan M, Prasad R, Bansil A 2012 Phys. Rev. B 86 115208 Google Scholar
[11]	Wang Z, Weng H, Wu Q, Dai X, Fang Z 2013 Phys. Rev. B 88 125427 Google Scholar
[12]	Liu J, Vanderbilt D 2014 Phys. Rev. B 90 155316 Google Scholar
[13]	Bulmash D, Liu C X, Qi X L 2014 Phys. Rev. B 89 081106 Google Scholar
[14]	Brahlek M, Bansal N, Koirala N, Xu S Y, Neupane M, Liu C, Hasan M Z, Oh S 2012 Phys. Rev. Lett. 109 186403 Google Scholar
[15]	Wu L, Brahlek M, Aguilar R V, Stier A, Morris C, Lubashevsky Y, Bilbro L, Bansal N, Oh S, Armitage N 2013 Nat. Phys. 9 410 Google Scholar
[16]	Liu Z, Zhou B, Zhang Y, Wang Z, Weng H, Prabhakaran D, Mo S K, Shen Z, Fang Z, Dai X 2014 Science 343 864 Google Scholar
[17]	Xu S Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C C 2015 Science 349 613 Google Scholar
[18]	Liu Z, Jiang J, Zhou B, Wang Z, Zhang Y, Weng H, Prabhakaran D, Mo S K, Peng H, Dudin P 2014 Nat. Mater. 13 677 Google Scholar
[19]	Neupane M, Xu S Y, Sankar R, Alidoust N, Bian G, Liu C, Belopolski I, Chang T R, Jeng H T, Lin H 2014 Nat. Commun. 5 3786
[20]	Yi H, Wang Z, Chen C, Shi Y, Feng Y, Liang A, Xie Z, He S, He J, Peng Y 2014 Sci. Rep. 4 6106
[21]	Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava R J 2014 Phys. Rev. Lett. 113 027603 Google Scholar
[22]	Weng H, Fang C, Fang Z, Bernevig B A, Dai X 2015 Phys. Rev. X 5 011029
[23]	Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B, Alidoust N, Bian G, Neupane M, Zhang C 2015 Nat. Commun. 6 7373
[24]	Lv B, Weng H, Fu B, Wang X P, Miao H, Ma J, Richard P, Huang X, Zhao L, Chen G, et al. 2015 Phys. Rev. X 5 031013
[25]	Borisenko S, Evtushinsky D, Gibson Q, Yaresko A, Koepernik K, Kim T, Ali M, van den Brink J, Hoesch M, Fedorov A 2019 Nat. Commun. 10 3424 Google Scholar
[26]	Nielsen H B, Ninomiya M 1981 Nucl. Phys. B 185 20 Google Scholar
[27]	Nielsen H B, Ninomiya M 1983 Phys. Lett. B 130 389 Google Scholar
[28]	Son D, Spivak B 2013 Phys. Rev. B 88 104412 Google Scholar
[29]	Burkov A 2014 Phys. Rev. Lett. 113 247203 Google Scholar
[30]	Kharzeev D E, Yee H U 2013 Phys. Rev. B 88 115119 Google Scholar
[31]	Parameswaran S, Grover T, Abanin D, Pesin D, Vishwanath A 2014 Phys. Rev. X 4 031035
[32]	Zhou J, Chang H R, Xiao D 2015 Phys. Rev. B 91 035114 Google Scholar
[33]	Son D T, Yamamoto N 2012 Phys. Rev. Lett. 109 181602 Google Scholar
[34]	Stephanov M, Yin Y 2012 Phys. Rev. Lett. 109 162001 Google Scholar
[35]	Landsteiner K, Megias E, Pena-Benitez F 2011 Phys. Rev. Lett. 107 021601 Google Scholar
[36]	Chang M C, Yang M F 2015 Phys. Rev. B 91 115203 Google Scholar
[37]	Jiang Q D, Jiang H, Liu H, Sun Q F, Xie X 2015 Phys. Rev. Lett. 115 156602 Google Scholar
[38]	Jiang Q D, Jiang H, Liu H, Sun Q F, Xie X 2016 Phys. Rev. B 93 195165 Google Scholar
[39]	Chen C Z, Song J, Jiang H, Sun Q f, Wang Z, Xie X 2015 Phys. Rev. Lett. 115 246603 Google Scholar
[40]	Chen C Z, Liu H, Jiang H, Xie X 2016 Phys. Rev. B 93 165420 Google Scholar
[41]	Kim H J, Kim K S, Wang J F, Sasaki M, Satoh N, Ohnishi A, Kitaura M, Yang M, Li L 2013 Phys. Rev. Lett. 111 246603 Google Scholar
[42]	Kim K S, Kim H J, Sasaki M 2014 Phys. Rev. B 89 195137 Google Scholar
[43]	Li Q, Kharzeev D E, Zhang C, Huang Y, Pletikosić I, Fedorov A, Zhong R, Schneeloch J, Gu G, Valla T 2016 Nat. Phys. 12 550 Google Scholar
[44]	Chen R, Chen Z, Song X Y, Schneeloch J, Gu G, Wang F, Wang N 2015 Phys. Rev. Lett. 115 176404 Google Scholar
[45]	Zheng G, Lu J, Zhu X, Ning W, Han Y, Zhang H, Zhang J, Xi C, Yang J, Du H, et al. 2016 Phys. Rev. B 93 115414 Google Scholar
[46]	Xiong J, Kushwaha S K, Liang T, Krizan J W, Hirschberger M, Wang W, Cava R J, Ong N P 2015 Science 350 413 Google Scholar
[47]	Jeon S, Zhou B B, Gyenis A, Feldman B E, Kimchi I, Potter A C, Gibson Q D, Cava R J, Vishwanath A, Yazdani A 2014 Nat. Mater. 13 851 Google Scholar
[48]	Liang T, Gibson Q, Ali M N, Liu M, Cava R, Ong N 2015 Nat. Mater. 14 280 Google Scholar
[49]	Feng J, Pang Y, Wu D, Wang Z, Weng H, Li J, Dai X, Fang Z, Shi Y, Lu L 2015 Phys. Rev. B 92 081306 Google Scholar
[50]	He L, Hong X, Dong J, Pan J, Zhang Z, Zhang J, Li S 2014 Phys. Rev. Lett. 113 246402 Google Scholar
[51]	Zhao Y, Liu H, Zhang C, Wang H, Wang J, Lin Z, Xing Y, Lu H, Liu J, Wang Y, et al. 2015 Phys. Rev. X 5 031037
[52]	Cao J, Liang S, Zhang C, Liu Y, Huang J, Jin Z, Chen Z G, Wang Z, Wang Q, Zhao J 2015 Nat. Commun. 6 7779
[53]	Shekhar C, Nayak A K, Sun Y, Schmidt M, Nicklas M, Leermakers I, Zeitler U, Skourski Y, Wosnitza J, Liu Z 2015 Nat. Phys. 11 645 Google Scholar
[54]	Narayanan A, Watson M, Blake S, Bruyant N, Drigo L, Chen Y, Prabhakaran D, Yan B, Felser C, Kong T 2015 Phys. Rev. Lett. 114 117201 Google Scholar
[55]	Li C Z, Wang L X, Liu H, Wang J, Liao Z M, Yu D P 2015 Nat. Commun. 6 10137
[56]	Li H, He H, Lu H Z, Zhang H, Liu H, Ma R, Fan Z, Shen S Q, Wang J 2016 Nat. Commun. 7 10301
[57]	Zhang C, Zhang E, Liu Y, Chen Z G, Liang S, Cao J, Yuan X, Tang L, Li Q, Gu T, et al. 2015 arXiv: 1504.07698 [cond-mat]
[58]	Wang H, Wang H, Liu H, Lu H, Yang W, Jia S, Liu X J, Xie X, Wei J, Wang J 2016 Nat. Mater. 15 38 Google Scholar
[59]	Aggarwal L, Gaurav A, Thakur G S, Haque Z, Ganguli A K, Sheet G 2016 Nat. Mater. 15 32 Google Scholar
[60]	Huang X, Zhao L, Long Y, Wang P, Chen D, Yang Z, Liang H, Xue M, Weng H, Fang Z 2015 Phys. Rev. X 5 031023
[61]	Zhang C L, Xu S Y, Belopolski I, Yuan Z, Lin Z, Tong B, Bian G, Alidoust N, Lee C C, Huang S M 2016 Nat. Commun. 7 10735
[62]	Zhang C, Guo C, Lu H, Zhang X, Yuan Z, Lin Z, Wang J, Jia S 2015 Phys. Rev. B 92 041203 Google Scholar
[63]	Arnold F, Shekhar C, Wu S C, Sun Y, Dos Reis R D, Kumar N, Naumann M, Ajeesh M O, Schmidt M, Grushin A G 2016 Nat. Commun. 7 11615
[64]	Zhang C L, Xu S Y, Wang C, Lin Z, Du Z, Guo C, Lee C C, Lu H, Feng Y, Huang S M 2017 Nat. Phys. 13 979 Google Scholar
[65]	Yang X, Liu Y, Wang Z, Zheng Y, Xu Z A 2015 arXiv: 1506.03190 [cond-mat]
[66]	Li Y, Wang Z, Li P, Yang X, Shen Z, Sheng F, Li X, Lu Y, Zheng Y, Xu Z A 2017 Front. Phys. 12 127205 Google Scholar
[67]	Wang Z, Zheng Y, Shen Z, Lu Y, Fang H, Sheng F, Zhou Y, Yang X, Li Y, Feng C, et al. 2016 Phys. Rev. B 93 121112 Google Scholar
[68]	Wang H, Li C K, Liu H, Yan J, Wang J, Liu J, Lin Z, Li Y, Wang Y, Li L 2016 Phys. Rev. B 93 165127 Google Scholar
[69]	Lu H Z, Shen S Q 2017 Front. Phys. 12 127201 Google Scholar
[70]	Sun H P, Lu H Z 2019 Front. Phys. 14 33405 Google Scholar
[71]	Lu H Z, Shi J, Shen S Q 2011 Phys. Rev. Lett. 107 076801 Google Scholar
[72]	Lu H Z, Shen S Q 2014 Phys. Rev. Lett. 112 146601 Google Scholar
[73]	Lu H Z, Shen S Q 2015 Phys. Rev. B 92 035203 Google Scholar
[74]	Lu H Z, Zhang S B, Shen S Q 2015 Phys. Rev. B 92 045203 Google Scholar
[75]	Dai X, Lu H Z, Shen S Q, Yao H 2016 Phys. Rev. B 93 161110 Google Scholar
[76]	Zhang S B, Lu H Z, Shen S Q 2016 New J. Phys. 18 053039 Google Scholar
[77]	Wang C, Lu H Z, Shen S Q 2016 Phys. Rev. Lett. 117 077201 Google Scholar
[78]	Wang C, Sun H P, Lu H Z, Xie X 2017 Phys. Rev. Lett. 119 136806 Google Scholar
[79]	Li C, Wang C, Wan B, Wan X, Lu H Z, Xie X 2018 Phys. Rev. Lett. 120 146602 Google Scholar
[80]	Dai X, Du Z, Lu H Z 2017 Phys. Rev. Lett. 119 166601 Google Scholar
[81]	Chen Y, Lu H Z, Xie X 2018 Phys. Rev. Lett. 121 036602 Google Scholar
[82]	Du Z, Wang C, Lu H Z, Xie X 2018 Phys. Rev. Lett. 121 266601 Google Scholar
[83]	Du Z, Wang C, Li S, Lu H Z, Xie X 2019 Nat. Commun. 10 3047
[84]	Cao Z, Zhang H, Lü H F, He W X, Lu H Z, Xie X 2019 Phys. Rev. Lett. 122 147701 Google Scholar
[85]	Zhang C L, Wang C, Yuan Z, Xu X, Wang G, Lee C C, Pi L, Xi C, Lin H, Harrison N 2019 Nat. Commun. 10 1028
[86]	Zhang J, Wang C, Guo C, et al. 2018 Phys. Rev. Lett. 123 196602
[87]	Qin Fang, Li Shuai, Du Z Z, Wang C M, Zhang W Q, Yu D P, Lu H Z, Xie X C 2020 Phys. Rev. Lett. 125 206601 Google Scholar
[88]	Lu H Z, Shen S Q 2016 Chin. Phys. B 25 117202 Google Scholar
[89]	Hosur P, Qi X 2013 C. R. Phys. 14 857 Google Scholar
[90]	Weng H, Dai X, Fang Z 2016 J. Phys. Condes. Matter 28 303001 Google Scholar
[91]	Yan B, Felser C 2017 Annu. Rev. Condens. Matter Phys. 8 337 Google Scholar
[92]	Armitage N, Mele E, Vishwanath A 2018 Rev. Mod. Phys. 90 015001 Google Scholar
[93]	Wang H, Wang J 2018 Chin. Phys. B 27 107402 Google Scholar
[94]	Shen S Q 2017 Topological Insulators: Dirac Equation in Condensed Matter (Vol. 187) (Singapore: Springer) pp207−229
[95]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[96]	Asbóth J K, Oroszlány L, Pályi A P 2016 A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions (Vol. 919) (Heidelberg, New York, London: Springer) p33
[97]	Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B 81 115407 Google Scholar
[98]	Shan W Y, Lu H Z, Shen S Q 2010 New J. Phys. 12 043048 Google Scholar
[99]	Shen S Q, Shan W Y, Lu H Z 2011 Spin 01 33 Google Scholar
[100]	Shen S Q, Ma M, Xie X, Zhang F C 2004 Phys. Rev. Lett. 92 256603 Google Scholar
[101]	Shen S Q, Bao Y J, Ma M, Xie X, Zhang F C 2005 Phys. Rev. B 71 155316 Google Scholar
[102]	Sakurai J, Napolitano J 2017 Modern Quantum Mechanics (Cambridge: Cambridge University Press) pp105−108
[103]	Yang L, Liu Z, Sun Y, Peng H, Yang H, Zhang T, Zhou B, Zhang Y, Guo Y, Rahn M, et al. 2015 Nat. Phys. 11 728 Google Scholar
[104]	Xu S Y, Alidoust N, Belopolski I, Yuan Z, Bian G, Chang T R, Zheng H, Strocov V N, Sanchez D S, Chang G 2015 Nat. Phys. 11 748 Google Scholar
[105]	Xu N, Weng H, Lv B, Matt C E, Park J, Bisti F, Strocov V N, Gawryluk D, Pomjakushina E, Conder K 2016 Nat. Commun. 7 11006
[106]	Guan T, Lin C, Yang C, Shi Y, Ren C, Li Y, Weng H, Dai X, Fang Z, Yan S 2015 Phys. Rev. Lett. 115 087002 Google Scholar
[107]	Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Chang T R, Wang B, Alidoust N, Bian G, Neupane M 2016 Proc. Natl. Acad. Sci. 113 1180 Google Scholar
[108]	Burkov A, Hook M, Balents L 2011 Phys. Rev. B 84 235126 Google Scholar
[109]	Chiu C K, Schnyder A P 2014 Phys. Rev. B 90 205136 Google Scholar
[110]	Fang C, Weng H, Dai X, Fang Z 2016 Chin. Phys. B 25 117106 Google Scholar
[111]	Yang B J, Bojesen T A, Morimoto T, Furusaki A 2017 Phys. Rev. B 95 075135 Google Scholar
[112]	Chen Y, Xie Y, Yang S A, Pan H, Zhang F, Cohen M L, Zhang S 2015 Nano Lett. 15 6974 Google Scholar
[113]	Bzdušek T, Wu Q, Rüegg A, Sigrist M, Soluyanov A A 2016 Nature 538 75 Google Scholar
[114]	Feng X, Yue C, Song Z, Wu Q, Wen B 2018 Phys. Rev. Mater. 2 014202 Google Scholar
[115]	Yi C J, Lv B, Wu Q, Fu B B, Gao X, Yang M, Peng X L, Li M, Huang Y B, Richard P 2018 Phys. Rev. B 97 201107 Google Scholar
[116]	Chen W, Luo K, Li L, Zilberberg O 2018 Phys. Rev. Lett. 121 166802 Google Scholar
[117]	Zhu Z, Chang T R, Huang C Y, Pan H, Nie X A, Wang X Z, Jin Z T, Xu S Y, Huang S M, Guan D D 2018 Nat. Commun. 9 4153
[118]	Chen W, Lado J L 2019 Phys. Rev. Lett. 122 016803 Google Scholar
[119]	Weng H, Liang Y, Xu Q, Yu R, Fang Z, Dai X, Kawazoe Y 2015 Phys. Rev. B 92 045108 Google Scholar
[120]	Yu R, Weng H, Fang Z, Dai X, Hu X 2015 Phys. Rev. Lett. 115 036807 Google Scholar
[121]	Kim Y, Wieder B J, Kane C, Rappe A M 2015 Phys. Rev. Lett. 115 036806 Google Scholar
[122]	Fang C, Chen Y, Kee H Y, Fu L 2015 Phys. Rev. B 92 081201 Google Scholar
[123]	Chen Y, Lu Y M, Kee H Y 2015 Nat. Commun. 6 6593
[124]	Bian G, Chang T R, Zheng H, Velury S, Xu S Y, Neupert T, Chiu C K, Huang S M, Sanchez D S, Belopolski I 2016 Phys. Rev. B 93 121113 Google Scholar
[125]	Xie L S, Schoop L M, Seibel E M, Gibson Q D, Xie W, Cava R J 2015 APL Mater. 3 083602 Google Scholar
[126]	Chan Y H, Chiu C K, Chou M, Schnyder A P 2016 Phys. Rev. B 93 205132 Google Scholar
[127]	Du Y, Tang F, Wang D, Sheng L, Kan E j, Duan C G, Savrasov S Y, Wan X 2017 npj Quantum Mater. 2 1 Google Scholar
[128]	Zhao J, Yu R, Weng H, Fang Z 2016 Phys. Rev. B 94 195104 Google Scholar
[129]	Yamakage A, Yamakawa Y, Tanaka Y, Okamoto Y 2016 J. Phys. Soc. Jpn. 85 013708 Google Scholar
[130]	Xu Q, Yu R, Fang Z, Dai X, Weng H 2017 Phys. Rev. B 95 045136 Google Scholar
[131]	Jin Y J, Wang R, Zhao J Z, Du Y P, Zheng C D, Gan L Y, Liu J F, Xu H, Tong S 2017 Nanoscale 9 13112 Google Scholar
[132]	Zhu Z, Li M, Li J 2016 Phys. Rev. B 94 155121 Google Scholar
[133]	Liang Q F, Zhou J, Yu R, Wang Z, Weng H 2016 Phys. Rev. B 93 085427 Google Scholar
[134]	Zeng M, Fang C, Chang G, Chen Y A, Hsieh T, Bansil A, Lin H, Fu L 2015 arXiv: 1504.03492 [cond-mat]
[135]	Hirayama M, Okugawa R, Miyake T, Murakami S 2017 Nat. Commun. 8 14022
[136]	Huang H, Liu J, Vanderbilt D, Duan W 2016 Phys. Rev. B 93 201114 Google Scholar
[137]	Li R, Ma H, Cheng X, Wang S, Li D, Zhang Z, Li Y, Chen X Q 2016 Phys. Rev. Lett. 117 096401 Google Scholar
[138]	Wang J T, Weng H, Nie S, Fang Z, Kawazoe Y, Chen C 2016 Phys. Rev. Lett. 116 195501 Google Scholar
[139]	Sun Y, Zhang Y, Liu C X, Felser C, Yan B 2017 Phys. Rev. B 95 235104 Google Scholar
[140]	Schoop L M, Ali M N, Straßer C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S, Lotsch B V, Ast C R 2016 Nat. Commun. 7 11696
[141]	Neupane M, Belopolski I, Hosen M M, Sanchez D S, Sankar R, Szlawska M, Xu S Y, Dimitri K, Dhakal N, Maldonado P 2016 Phys. Rev. B 93 201104 Google Scholar
[142]	Chen C, Xu X, Jiang J, Wu S C, Qi Y, Yang L, Wang M, Sun Y, Schröter N, Yang H 2017 Phys. Rev. B 95 125126 Google Scholar
[143]	Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I 2016 Nat. Commun. 7 10556
[144]	Chang T R, Chen P J, Bian G, Huang S M, Zheng H, Neupert T, Sankar R, Xu S Y, Belopolski I, Chang G 2016 Phys. Rev. B 93 245130 Google Scholar
[145]	Ekahana S A, Wu S C, Jiang J, Okawa K, Prabhakaran D, Hwang C C, Mo S K, Sasagawa T, Felser C, Yan B 2017 New J. Phys. 19 065007 Google Scholar
[146]	Wu Y, Wang L L, Mun E, Johnson D D, Mou D, Huang L, Lee Y, Bud’ko S L, Canfield P C, Kaminski A 2016 Nat. Phys. 12 667 Google Scholar
[147]	Chen W, Lu H Z, Zilberberg O 2019 Phys. Rev. Lett. 122 196603 Google Scholar
[148]	Alexandradinata A, Glazman L 2018 Phys. Rev. B 97 144422 Google Scholar
[149]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[150]	Nechaev I, Krasovskii E 2016 Phys. Rev. B 94 201410 Google Scholar
[151]	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 2010 Nat. Phys. 6 584 Google Scholar
[152]	Wang J, Li H, Chang C, He K, Lee J S, Lu H, Sun Y, Ma X, Samarth N, Shen S 2012 Nano Res. 5 739 Google Scholar
[153]	He H, Liu H, Li B, Guo X, Xu Z, Xie M, Wang J 2013 Appl. Phys. Lett. 103 031606 Google Scholar
[154]	Wiedmann S, Jost A, Fauqué B, Van Dijk J, Meijer M, Khouri T, Pezzini S, Grauer S, Schreyeck S, Brüne C 2016 Phys. Rev. B 94 081302 Google Scholar
[155]	Wang L X, Yan Y, Zhang L, Liao Z M, Wu H C, Yu D P 2015 Nanoscale 7 16687 Google Scholar
[156]	Sun H P, Wang C M, Zhang S B, Chen R, Zhao Y, Liu C, Liu Q, Chen C, Lu H Z, Xie X C 2020 Phys. Rev. B 102 241406 Google Scholar
[157]	Klitzing K v, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[158]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[159]	Yasuda K, Wakatsuki R, Morimoto T, Yoshimi R, Tsukazaki A, Takahashi K, Ezawa M, Kawasaki M, Nagaosa N, Tokura Y 2016 Nat. Phys. 12 555 Google Scholar
[160]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[161]	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, et al. 2019 Nature 565 337 Google Scholar
[162]	Kang K, Li T, Sohn E, Shan J, Mak K F 2018 arXiv: 1809.08744 [cond-mat]
[163]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[164]	Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003 Google Scholar
[165]	Beenakker C 2013 Annu. Rev. Condens. Matter Phys. 4 113 Google Scholar
[166]	Stanescu T D, Tewari S 2013 J. Phys. Condes. Matter 25 233201 Google Scholar
[167]	Lutchyn R M, Sau J D, Sarma S D 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[168]	Oreg Y, Refael G, Von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[169]	Prada E, San-Jose P, Aguado R 2012 Phys. Rev. B 86 180503 Google Scholar
[170]	Sarma S D, Sau J D, Stanescu T D 2012 Phys. Rev. B 86 220506 Google Scholar
[171]	Rainis D, Trifunovic L, Klinovaja J, Loss D 2013 Phys. Rev. B 87 024515 Google Scholar
[172]	Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C 2016 Nature 531 206 Google Scholar
[173]	Sherman D, Yodh J, Albrecht S M, Nygård J, Krogstrup P, Marcus C M 2017 Nat. Nanotechnol. 12 212 Google Scholar
[174]	Albrecht S, Hansen E, Higginbotham A P, Kuemmeth F, Jespersen T, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus C 2017 Phys. Rev. Lett. 118 137701 Google Scholar
[175]	Vaitiekėnas S, Whiticar A M, Deng M T, Krizek F, Sestoft J E, Palmstrøm C, Martí-Sànchez S, Arbiol J, Krogstrup P, Casparis L 2018 Phys. Rev. Lett. 121 147701 Google Scholar
[176]	O’Farrell E, Drachmann A, Hell M, Fornieri A, Whiticar A, Hansen E, Gronin S, Gardner G, Thomas C, Manfra M 2018 Phys. Rev. Lett. 121 256803 Google Scholar
[177]	Shen J, Heedt S, Borsoi F, Van Heck B, Gazibegovic S, Veld R L O, Car D, Logan J A, Pendharkar M, Ramakers S J 2018 Nat. Commun. 9 4801
[178]	Sánchez D, Serra L 2006 Phys. Rev. B 74 153313 Google Scholar
[179]	Sánchez D, Serra L, Choi M S 2008 Phys. Rev. B 77 035315 Google Scholar
[180]	Glazov M, Sherman E Y 2011 Phys. Rev. Lett. 107 156602 Google Scholar
[181]	Bommer J D, Zhang H, Gül Ö, Nijholt B, Wimmer M, Rybakov F N, Garaud J, Rodic D, Babaev E, Troyer M 2019 Phys. Rev. Lett. 122 187702 Google Scholar
[182]	Vaitiekėnas S, Deng M T, Nygård J, Krogstrup P, Marcus C 2018 Phys. Rev. Lett. 121 037703 Google Scholar
[183]	de Moor M W, Bommer J D, Xu D, Winkler G W, Antipov A E, Bargerbos A, Wang G, Van Loo N, het Veld R L O, Gazibegovic S 2018 New J. Phys. 20 103049 Google Scholar
[184]	Stanescu T D, Lutchyn R M, Sarma S D 2011 Phys. Rev. B 84 144522 Google Scholar
[185]	Reeg C, Loss D, Klinovaja J 2018 Phys. Rev. B 97 165425 Google Scholar
[186]	Van Heck B, Lutchyn R, Glazman L 2016 Phys. Rev. B 93 235431 Google Scholar
[187]	Fu L 2010 Phys. Rev. Lett. 104 056402 Google Scholar
[188]	Hützen R, Zazunov A, Braunecker B, Yeyati A L, Egger R 2012 Phys. Rev. Lett. 109 166403 Google Scholar
[189]	Higginbotham A P, Albrecht S M, Kiršanskas G, Chang W, Kuemmeth F, Krogstrup P, Jespersen T S, Nygård J, Flensberg K, Marcus C M 2015 Nat. Phys. 11 1017 Google Scholar
[190]	Lü H F, Lu H Z, Shen S Q 2016 Phys. Rev. B 93 245418 Google Scholar
[191]	Lee P A, Ramakrishnan T 1985 Rev. Mod. Phys. 57 287 Google Scholar
[192]	Fu B, Wang H W, Shen S Q 2019 Phys. Rev. Lett. 122 246601 Google Scholar
[193]	Wang H W, Fu B, Shen S Q 2020 Phys. Rev. Lett. 124 206603 Google Scholar
[194]	Dyson F J 1962 J. Math. Phys. 3 140 Google Scholar
[195]	Hikami S, Larkin A I, Nagaoka Y 1980 Prog. Theor. Phys. 63 707 Google Scholar
[196]	McCann E, Kechedzhi K, Fal’ko V I, Suzuura H, Ando T, Altshuler B 2006 Phys. Rev. Lett. 97 146805 Google Scholar
[197]	Altshuler B L, Aronov A G, Lee P 1980 Phys. Rev. Lett. 44 1288 Google Scholar
[198]	Fukuyama H 1980 J. Phys. Soc. Jpn. 48 2169 Google Scholar
[199]	Shan W Y, Lu H Z, Shen S Q 2012 Phys. Rev. B 86 125303 Google Scholar
[200]	Berry M V 1984 Proc. R. Soc. A-Math. Phys. 392 45
[201]	Shon N H, Ando T 1998 J. Phys. Soc. Jpn. 67 2421 Google Scholar
[202]	Suzuura H, Ando T 2002 Phys. Rev. Lett. 89 266603 Google Scholar
[203]	Altland A, Zirnbauer M R 1997 Phys. Rev. B 55 1142 Google Scholar
[204]	Akkermans E, Montambaux G 2007 Mesoscopic Physics of Electrons and Photons (Cambridge: Cambridge university press) pp97−100
[205]	Cao H, Tian J, Miotkowski I, Shen T, Hu J, Qiao S, Chen Y P 2012 Phys. Rev. Lett. 108 216803 Google Scholar
[206]	Checkelsky J G, Hor Y S, Liu M H, Qu D X, Cava R J, Ong N 2009 Phys. Rev. Lett. 103 246601 Google Scholar
[207]	Peng H, Lai K, Kong D, Meister S, Chen Y, Qi X L, Zhang S C, Shen Z X, Cui Y 2010 Nat. Mater. 9 225 Google Scholar
[208]	Chen J, Qin H, Yang F, Liu J, Guan T, Qu F, Zhang G, Shi J, Xie X, Yang C, et al. 2010 Phys. Rev. Lett. 105 176602 Google Scholar
[209]	Checkelsky J G, Hor Y S, Cava R J, Ong N 2011 Phys. Rev. Lett. 106 196801 Google Scholar
[210]	Adler S L 1969 Phys. Rev. 177 2426 Google Scholar
[211]	Bell J S, Jackiw R 1969 Il Nuovo Cimento A (1965-1970) 60 47 Google Scholar
[212]	Burkov A 2017 Phys. Rev. B 96 041110 Google Scholar
[213]	Nandy S, Sharma G, Taraphder A, Tewari S 2017 Phys. Rev. Lett. 119 176804 Google Scholar
[214]	Kumar N, Guin S N, Felser C, Shekhar C 2018 Phys. Rev. B 98 041103 Google Scholar
[215]	Wu M, Zheng G, Chu W, Liu Y, Gao W, Zhang H, Lu J, Han Y, Zhou J, Ning W 2018 Phys. Rev. B 98 161110 Google Scholar
[216]	Li H, Wang H W, He H, Wang J, Shen S Q 2018 Phys. Rev. B 97 201110 Google Scholar
[217]	Ma D, Jiang H, Liu H, Xie X 2019 Phys. Rev. B 99 115121 Google Scholar
[218]	Chang M C, Niu Q 1995 Phys. Rev. Lett. 75 1348 Google Scholar
[219]	Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915 Google Scholar
[220]	Jian H Z, Hua J, Qian N, Jun R S 2013 Chin. Phys. Lett. 30 027101 Google Scholar
[221]	Goswami P, Tewari S 2013 Phys. Rev. B 88 245107 Google Scholar
[222]	Zyuzin A, Burkov A 2012 Phys. Rev. B 86 115133 Google Scholar
[223]	Yip S K 2015 arXiv: 1508.01010 [cond-mat]
[224]	Zhang C, Zhang E, Wang W, Liu Y, Chen Z G, Lu S, Liang S, Cao J, Yuan X, Tang L 2017 Nat. Commun. 8 13741
[225]	Breunig O, Wang Z, Taskin A, Lux J, Rosch A, Ando Y 2017 Nat. Commun. 8 15545
[226]	Assaf B, Phuphachong T, Kampert E, Volobuev V, Mandal P, Sánchez-Barriga J, Rader O, Bauer G, Springholz G, De Vaulchier L 2017 Phys. Rev. Lett. 119 106602 Google Scholar
[227]	Zhang M, Wang H, Mu K, Wang P, Niu W, Zhang S, Xiao G, Chen Y, Tong T, Fu D 2018 ACS Nano 12 1537 Google Scholar
[228]	Fleckenstein C, Ziani N T, Trauzettel B 2016 Phys. Rev. B 94 241406 Google Scholar
[229]	Culcer D 2012 Physica E 44 860 Google Scholar
[230]	Mahan G D 2013 Many-particle Physics (New York: Springer Science & Business Media) pp160−174
[231]	Wolos A, Szyszko S, Drabinska A, Kaminska M, Strzelecka S, Hruban A, Materna A, Piersa M, Borysiuk J, Sobczak K 2016 Phys. Rev. B 93 155114 Google Scholar
[232]	Wang J, DaSilva A M, Chang C Z, He K, Jain J K, Samarth N, Ma X C, Xue Q K, Chan M H 2011 Phys. Rev. B 83 245438 Google Scholar
[233]	He H T, Wang G, Zhang T, Sou I K, Wong G K, Wang J N, Lu H Z, Shen S Q, Zhang F C 2011 Phys. Rev. Lett. 106 166805 Google Scholar
[234]	Morimoto T, Zhong S, Orenstein J, Moore J E 2016 Phys. Rev. B 94 245121 Google Scholar
[235]	Gao Y, Yang S A, Niu Q 2017 Phys. Rev. B 95 165135 Google Scholar
[236]	Gao Y, Yang S A, Niu Q 2014 Phys. Rev. Lett. 112 166601 Google Scholar
[237]	Gao Y, Yang S A, Niu Q 2015 Phys. Rev. B 91 214405 Google Scholar
[238]	Goswami P, Pixley J, Sarma S D 2015 Phys. Rev. B 92 075205 Google Scholar
[239]	Andreev A, Spivak B 2018 Phys. Rev. Lett. 120 026601 Google Scholar
[240]	Fu B, Wang H W, Shen S Q 2020 Phys. Rev. B 101 125203 Google Scholar
[241]	Shoenberg D 1984 Magnetic Oscillations in Metals (Cambridge: Cambridge University Press) pp36−67
[242]	Mikitik G, Sharlai Y V 1999 Phys. Rev. Lett. 82 2147 Google Scholar
[243]	Shoenberg D, Stiles P 1964 Proc. R. Soc. A-Math. Phys. 281 62
[244]	Luk’yanchuk I A, Kopelevich Y 2004 Phys. Rev. Lett. 93 166402 Google Scholar
[245]	Novak M, Sasaki S, Segawa K, Ando Y 2015 Phys. Rev. B 91 041203 Google Scholar
[246]	Du J, Wang H, Chen Q, Mao Q, Khan R, Xu B, Zhou Y, Zhang Y, Yang J, Chen B 2016 Sci. China-Phys. Mech. Astron. 59 657406 Google Scholar
[247]	Zhang C L, Yuan Z, Jiang Q D, Tong B, Zhang C, Xie X, Jia S 2017 Phys. Rev. B 95 085202 Google Scholar
[248]	Park J, Lee G, Wolff-Fabris F, Koh Y, Eom M, Kim Y K, Farhan M, Jo Y, Kim C, Shim J 2011 Phys. Rev. Lett. 107 126402 Google Scholar
[249]	Xiang F X, Wang X L, Veldhorst M, Dou S X, Fuhrer M S 2015 Phys. Rev. B 92 035123 Google Scholar
[250]	Tafti F, Gibson Q, Kushwaha S, Haldolaarachchige N, Cava R 2016 Nat. Phys. 12 272 Google Scholar
[251]	Luo Y, Ghimire N J, Wartenbe M, Choi H, Neupane M, McDonald R, Bauer E, Zhu J, Thompson J, Ronning F 2015 Phys. Rev. B 92 205134 Google Scholar
[252]	Arnold F, Naumann M, Wu S C, Sun Y, Schmidt M, Borrmann H, Felser C, Yan B, Hassinger E 2016 Phys. Rev. Lett. 117 146401 Google Scholar
[253]	Klotz J, Wu S C, Shekhar C, Sun Y, Schmidt M, Nicklas M, Baenitz M, Uhlarz M, Wosnitza J, Felser C 2016 Phys. Rev. B 93 121105 Google Scholar
[254]	dos Reis R, Wu S, Sun Y, Ajeesh M, Shekhar C, Schmidt M, Felser C, Yan B, Nicklas M 2016 Phys. Rev. B 93 205102 Google Scholar
[255]	Sergelius P, Gooth J, Bäßler S, Zierold R, Wiegand C, Niemann A, Reith H, Shekhar C, Felser C, Yan B 2016 Sci. Rep. 6 33859
[256]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[257]	Murakawa H, Bahramy M, Tokunaga M, Kohama Y, Bell C, Kaneko Y, Nagaosa N, Hwang H, Tokura Y 2013 Science 342 1490 Google Scholar
[258]	Kumar N, Manna K, Qi Y, Wu S C, Wang L, Yan B, Felser C, Shekhar C 2017 Phys. Rev. B 95 121109 Google Scholar
[259]	Singha R, Pariari A K, Satpati B, Mandal P 2017 Proc. Natl. Acad. Sci. 114 2468 Google Scholar
[260]	Ali M N, Schoop L M, Garg C, Lippmann J M, Lara E, Lotsch B, Parkin S S 2016 Sci. Adv. 2 e1601742 Google Scholar
[261]	Wang X, Pan X, Gao M, Yu J, Jiang J, Zhang J, Zuo H, Zhang M, Wei Z, Niu W 2016 Adv. Electron. Mater. 2
[262]	Lv Y Y, Zhang B B, Li X, Yao S H, Chen Y, Zhou J, Zhang S T, Lu M H, Chen Y F 2016 Appl. Phys. Lett. 108 244101 Google Scholar
[263]	Hu J, Tang Z, Liu J, Zhu Y, Wei J, Mao Z 2017 Phys. Rev. B 96 045127 Google Scholar
[264]	Pan H, Tong B, Yu J, Wang J, Fu D, Zhang S, Wu B, Wan X, Zhang C, Wang X 2018 Sci. Rep. 8 1 Google Scholar
[265]	Hu J, Tang Z, Liu J, Liu X, Zhu Y, Graf D, Myhro K, Tran S, Lau C N, Wei J 2016 Phys. Rev. Lett. 117 016602 Google Scholar
[266]	Hu J, Zhu Y, Graf D, Tang Z, Liu J, Mao Z 2017 Phys. Rev. B 95 205134 Google Scholar
[267]	Qu D X, Hor Y S, Xiong J, Cava R J, Ong N P 2010 Science 329 821 Google Scholar
[268]	Charbonneau M, Van Vliet K, Vasilopoulos P 1982 J. Math. Phys. 23 318 Google Scholar
[269]	Vasilopoulos P, Van Vliet C M 1984 J. Math. Phys. 25 1391 Google Scholar
[270]	Wang C, Lei X 2012 Phys. Rev. B 86 035442 Google Scholar
[271]	Wang C, Lei X 2015 Phys. Rev. B 92 125303 Google Scholar
[272]	Datta S 1997 Electronic Transport in Mesoscopic Dystems (Cambridge: Cambridge university press) pp23−24
[273]	Vasko F T, Raichev O E 2006 Quantum Kinetic Theory and Applications: Electrons, Photons, Phonons (New York: Springer Science & Business Media) pp99−147
[274]	Abrikosov A 1998 Phys. Rev. B 58 2788
[275]	Liu Z, Yang L, Sun Y, Zhang T, Peng H, Yang H, Chen C, Zhang Y, Guo Y, Prabhakaran D 2016 Nat. Mater. 15 27 Google Scholar
[276]	Xiong J, Kushwaha S, Krizan J, Liang T, Cava R J, Ong N P 2016 EPL 114 27002 Google Scholar
[277]	Hu J, Liu J, Graf D, Radmanesh S, Adams D, Chuang A, Wang Y, Chiorescu I, Wei J, Spinu L 2016 Sci. Rep. 6 18674 Google Scholar
[278]	Phillips M, Aji V 2014 Phys. Rev. B 90 115111 Google Scholar
[279]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[280]	Novoselov K, Geim A, Morozov S, Jiang D, Katsnelson M, Grigorieva I, Dubonos S, Firsov A 2005 Nature 438 197 Google Scholar
[281]	Xu Y, Miotkowski I, Liu C, Tian J, Nam H, Alidoust N, Hu J, Shih C K, Hasan M Z, Chen Y P 2014 Nat. Phys. 10 956 Google Scholar
[282]	Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 6627
[283]	Lu H Z 2019 Natl. Sci. Rev. 6 208 Google Scholar
[284]	Hosur P 2012 Phys. Rev. B 86 195102 Google Scholar
[285]	Baum Y, Berg E, Parameswaran S, Stern A 2015 Phys. Rev. X 5 041046
[286]	Gorbar E, Miransky V, Shovkovy I, Sukhachov P 2016 Phys. Rev. B 93 235127 Google Scholar
[287]	Ominato Y, Koshino M 2016 Phys. Rev. B 93 245304 Google Scholar
[288]	McCormick T M, Watzman S J, Heremans J P, Trivedi N 2018 Phys. Rev. B 97 195152 Google Scholar
[289]	Moll P J, Nair N L, Helm T, Potter A C, Kimchi I, Vishwanath A, Analytis J G 2016 Nature 535 266 Google Scholar
[290]	Ruan J, Jian S K, Yao H, Zhang H, Zhang S C, Xing D 2016 Nat. Commun. 7 11136
[291]	Potter A C, Kimchi I, Vishwanath A 2014 Nat. Commun. 5 5161
[292]	Xu S Y, Belopolski I, Sanchez D S, Neupane M, Chang G, Yaji K, Yuan Z, Zhang C, Kuroda K, Bian G 2016 Phys. Rev. Lett. 116 096801 Google Scholar
[293]	Belopolski I, Xu S Y, Sanchez D S, Chang G, Guo C, Neupane M, Zheng H, Lee C C, Huang S M, Bian G 2016 Phys. Rev. Lett. 116 066802 Google Scholar
[294]	Belopolski I, Xu S Y, Ishida Y, Pan X, Yu P, Sanchez D S, Zheng H, Neupane M, Alidoust N, Chang G 2016 Phys. Rev. B 94 085127 Google Scholar
[295]	Xu S Y, Belopolski I, Sanchez D S, Zhang C, Chang G, Guo C, Bian G, Yuan Z, Lu H, Chang T R 2015 Sci. Adv. 1 e1501092 Google Scholar
[296]	Uchida M, Nakazawa Y, Nishihaya S, Akiba K, Kriener M, Kozuka Y, Miyake A, Taguchi Y, Tokunaga M, Nagaosa N 2017 Nat. Commun. 8 2274
[297]	Schumann T, Galletti L, Kealhofer D A, Kim H, Goyal M, Stemmer S 2018 Phys. Rev. Lett. 120 016801 Google Scholar
[298]	Zhang C, Zhang Y, Yuan X, Lu S, Zhang J, Narayan A, Liu Y, Zhang H, Ni Z, Liu R 2019 Nature 565 331 Google Scholar
[299]	Gusynin V, Sharapov S 2005 Phys. Rev. Lett. 95 146801 Google Scholar
[300]	Zyuzin A, Burkov A 2011 Phys. Rev. B 83 195413 Google Scholar
[301]	Zhang S B, Zhang Y Y, Shen S Q 2014 Phys. Rev. B 90 115305 Google Scholar
[302]	Zhang S B, Lu H Z, Shen S Q 2015 Sci. Rep. 5 13277 Google Scholar
[303]	Pertsova A, Canali C M, MacDonald A 2016 Phys. Rev. B 94 121409 Google Scholar
[304]	Zheng H, Xu S Y, Bian G, Guo C, Chang G, Sanchez D S, Belopolski I, Lee C C, Huang S M, Zhang X 2016 ACS Nano 10 1378 Google Scholar
[305]	Ma E Y, Calvo M R, Wang J, Lian B, Mühlbauer M, Brüne C, Cui Y T, Lai K, Kundhikanjana W, Yang Y 2015 Nat. Commun. 6 7252
[306]	Li H, Liu H, Jiang H, Xie X 2020 Phys. Rev. Lett. 125 036602 Google Scholar
[307]	Zhang C, Narayan A, Lu S, Zhang J, Zhang H, Ni Z, Yuan X, Liu Y, Park J H, Zhang E 2017 Nat. Commun. 8 1272
[308]	Lin B C, Wang S, Wiedmann S, Lu J M, Zheng W Z, Yu D, Liao Z M 2019 Phys. Rev. Lett. 122 036602 Google Scholar
[309]	Halperin B I 1987 Jpn. J. Appl. Phys. 26 1913 Google Scholar
[310]	Tang F, Ren Y, Wang P, Zhong R, Schneeloch J, Yang S A, Yang K, Lee P A, Gu G, Qiao Z 2019 Nature 569 537 Google Scholar
[311]	Song Z, Fang Z, Dai X 2017 Phys. Rev. B 96 235104 Google Scholar
[312]	Pan Z, Shindou R 2019 Phys. Rev. B 100 165124 Google Scholar
[313]	Roy B, Sau J D, Sarma S D 2014 Phys. Rev. B 89 165119 Google Scholar
[314]	Grüner G 1988 Rev. Mod. Phys. 60 1129 Google Scholar
[315]	Aji V 2012 Phys. Rev. B 85 241101 Google Scholar
[316]	Ominato Y, Koshino M 2014 Phys. Rev. B 89 054202 Google Scholar
[317]	Song J C, Refael G, Lee P A 2015 Phys. Rev. B 92 180204 Google Scholar
[318]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[319]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[320]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[321]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L 2013 Science 340 167 Google Scholar
[322]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[323]	Akhmerov A, Nilsson J, Beenakker C 2009 Phys. Rev. Lett. 102 216404 Google Scholar
[324]	Belopolski I, Xu S Y, Koirala N, Liu C, Bian G, Strocov V N, Chang G, Neupane M, Alidoust N, Sanchez D 2017 Sci. Adv. 3 e1501692 Google Scholar
[325]	Chiu C K, Bian G, Zheng H, Yin J X, Zhang S S, Sanchez D, Belopolski I, Xu S Y, Hasan M Z 2018 EPL 123 47005 Google Scholar
[326]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[327]	Büttner B, Liu C, Tkachov G, Novik E, Brüne C, Buhmann H, Hankiewicz E, Recher P, Trauzettel B, Zhang S 2011 Nat. Phys. 7 418 Google Scholar
[328]	Mani A, Benjamin C 2017 Sci. Rep. 7 6954
[329]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002
[330]	Liu Y, Yuan X, Zhang C, Jin Z, Narayan A, Luo C, Chen Z, Yang L, Zou J, Wu X 2016 Nat. Commun. 7 12516
[331]	Zhang W, Yu R, Feng W, Yao Y, Weng H, Dai X, Fang Z 2011 Phys. Rev. Lett. 106 156808 Google Scholar
[332]	Sebastian S E, Harrison N, Palm E, Murphy T, Mielke C, Liang R, Bonn D, Hardy W, Lonzarich G 2008 Nature 454 200 Google Scholar
[333]	Li L, Checkelsky J G, Hor Y S, Uher C, Hebard A F, Cava R J, Ong N 2008 Science 321 547 Google Scholar
[334]	Zhang Z, Wei W, Yang F, Zhu Z, Guo M, Feng Y, Yu D, Yao M, Harrison N, McDonald R 2015 Phys. Rev. B 92 235402 Google Scholar
[335]	Mikitik G, Sharlai Y V 2004 Phys. Rev. Lett. 93 106403 Google Scholar
[336]	Mikitik G, Sharlai Y V 1996 Low Temp. Phys. 22 585
[337]	Mikitik G, Sharlai Y V 2016 Phys. Rev. B 94 195123 Google Scholar
[338]	Moll P J, Potter A C, Nair N L, Ramshaw B, Modic K A, Riggs S, Zeng B, Ghimire N J, Bauer E D, Kealhofer R 2016 Nat. Commun. 7 12492
[339]	Koshino M, Hizbullah I F 2016 Phys. Rev. B 93 045201 Google Scholar
[340]	Chen Z G, Chen R, Zhong R, Schneeloch J, Zhang C, Huang Y, Qu F, Yu R, Li Q, Gu G 2017 Proc. Natl. Acad. Sci. 114 816 Google Scholar
[341]	Chen R, Zhang S, Schneeloch J, Zhang C, Li Q, Gu G, Wang N 2015 Phys. Rev. B 92 075107 Google Scholar
[342]	Wu R, Ma J Z, Nie S M, Zhao L X, Huang X, Yin J X, Fu B B, Richard P, Chen G F, Fang Z 2016 Phys. Rev. X 6 021017
[343]	Li X B, Huang W K, Lv Y Y, Zhang K W, Yang C L, Zhang B B, Chen Y, Yao S H, Zhou J, Lu M H 2016 Phys. Rev. Lett. 116 176803 Google Scholar
[344]	Xiong H, Sobota J, Yang S L, Soifer H, Gauthier A, Lu M H, Lv Y Y, Yao S H, Lu D, Hashimoto M 2017 Phys. Rev. B 95 195119 Google Scholar
[345]	Manzoni G, Gragnaniello L, Autès G, Kuhn T, Sterzi A, Cilento F, Zacchigna M, Enenkel V, Vobornik I, Barba L 2016 Phys. Rev. Lett. 117 237601 Google Scholar
[346]	Xu B, Zhao L, Marsik P, Sheveleva E, Lyzwa F, Dai Y, Chen G, Qiu X, Bernhard C 2018 Phys. Rev. Lett. 121 187401 Google Scholar
[347]	Zhang J, Guo C, Zhu X, Ma L, Zheng G, Wang Y, Pi L, Chen Y, Yuan H, Tian M 2017 Phys. Rev. Lett. 118 206601 Google Scholar
[348]	Jones T, Fuller W, Wieting T, Levy F 1982 Solid State Commun. 42 793 Google Scholar
[349]	Behnia K, Aubin H 2016 Rep. Prog. Phys. 79 046502 Google Scholar
[350]	Gooth J, Niemann A C, Meng T, Grushin A G, Landsteiner K, Gotsmann B, Menges F, Schmidt M, Shekhar C, Süß V 2017 Nature 547 324 Google Scholar
[351]	Behnia K, Méasson M A, Kopelevich Y 2007 Phys. Rev. Lett. 98 166602 Google Scholar
[352]	Fauqué B, Zhu Z, Murphy T, Behnia K 2011 Phys. Rev. Lett. 106 246405 Google Scholar
[353]	Fauqué B, Butch N P, Syers P, Paglione J, Wiedmann S, Collaudin A, Grena B, Zeitler U, Behnia K 2013 Phys. Rev. B 87 035133 Google Scholar
[354]	Liang T, Gibson Q, Xiong J, Hirschberger M, Koduvayur S P, Cava R J, Ong N P 2013 Nat. Commun. 4 1
[355]	Zhu Z, Lin X, Liu J, Fauqué B, Tao Q, Yang C, Shi Y, Behnia K 2015 Phys. Rev. Lett. 114 176601 Google Scholar
[356]	Jia Z, Li C, Li X, Shi J, Liao Z, Yu D, Wu X 2016 Nat. Commun. 7 13013
[357]	Liang T, Lin J, Gibson Q, Gao T, Hirschberger M, Liu M, Cava R J, Ong N P 2017 Phys. Rev. Lett. 118 136601 Google Scholar
[358]	Matusiak M, Cooper J, Kaczorowski D 2017 Nat. Commun. 8 15219
[359]	Watzman S J, McCormick T M, Shekhar C, Wu S C, Sun Y, Prakash A, Felser C, Trivedi N, Heremans J P 2018 Phys. Rev. B 97 161404 Google Scholar
[360]	Zhang Y, Wang C, Yu L, Liu G, Liang A, Huang J, Nie S, Sun X, Zhang Y, Shen B, et al. 2017 Nat. Commun. 8 15512 Google Scholar
[361]	Stockert U, Dos Reis R, Ajeesh M, Watzman S, Schmidt M, Shekhar C, Heremans J, Felser C, Baenitz M, Nicklas M 2017 J. Phys.-Condes. Matter 29 325701 Google Scholar
[362]	Wang J, Niu J, Yan B, Li X, Bi R, Yao Y, Yu D, Wu X 2018 Proc. Natl. Acad. Sci. 115 9145 Google Scholar
[363]	Skinner B, Fu L 2018 Sci. Adv. 4 eaat2621 Google Scholar
[364]	Raikh M, Shahbazyan T 1993 Phys. Rev. B 47 1522 Google Scholar
[365]	Pesin D, Mishchenko E, Levchenko A 2015 Phys. Rev. B 92 174202 Google Scholar
[366]	Wang H W, Fu B, Shen S Q 2018 Phys. Rev. B 98 081202 Google Scholar
[367]	Alexandradinata A, Glazman L 2017 Phys. Rev. Lett. 119 256601 Google Scholar
[368]	Alexandradinata A, Wang C, Duan W, Glazman L 2018 Phys. Rev. X 8 011027
[369]	Hoeller J, Alexandradinata A 2018 Phys. Rev. B 98 024310 Google Scholar
[370]	O’Brien T, Diez M, Beenakker C 2016 Phys. Rev. Lett. 116 236401 Google Scholar
[371]	Fei F, Bo X, Wang R, Wu B, Jiang J, Fu D, Gao M, Zheng H, Chen Y, Wang X 2017 Phys. Rev. B 96 041201 Google Scholar
[372]	Yang H, Moessner R, Lim L K 2018 Phys. Rev. B 97 165118 Google Scholar
[373]	Oroszlány L, Dóra B, Cserti J, Cortijo A 2018 Phys. Rev. B 97 205107 Google Scholar
[374]	Zhang Y, Bulmash D, Hosur P, Potter A C, Vishwanath A 2016 Sci. Rep. 6 23741 Google Scholar
[375]	Wang H, Liu H, Li Y, Liu Y, Wang J, Liu J, Dai J Y, Wang Y, Li L, Yan J 2018 Sci. Adv. 4 eaau5096 Google Scholar
[376]	Wang H, Liu Y, Liu Y, Xi C, Wang J, Liu J, Wang Y, Li L, Lau S P, Tian M 2019 Natl. Sci. Rev. 6 914 Google Scholar
[377]	Zhang P, Zhai H 2018 Front. Phys. 13 137204 Google Scholar
[378]	Liu H, Jiang H, Wang Z, Joynt R, Xie X 2018 arXiv: 1807.02459 [cond-mat]
[379]	Weng H, Fang C, Fang Z, Dai X 2016 Phys. Rev. B 93 241202 Google Scholar
[380]	Weng H, Fang C, Fang Z, Dai X 2016 Phys. Rev. B 94 165201 Google Scholar
[381]	Bradlyn B, Cano J, Wang Z, Vergniory M, Felser C, Cava R, Bernevig B A 2016 Science 353Google Scholar
[382]	Chang G, Xu S Y, Huang S M, Sanchez D S, Hsu C H, Bian G, Yu Z M, Belopolski I, Alidoust N, Zheng H 2017 Sci. Rep. 7 1688
[383]	Lv B, Feng Z L, Xu Q N, Gao X, Ma J Z, Kong L Y, Richard P, Huang Y B, Strocov V, Fang C 2017 Nature 546 627 Google Scholar
[384]	Ma J Z, He J B, Xu Y F, Lv B, Chen D, Zhu W L, Zhang S, Kong L Y, Gao X, Rong L Y 2018 Nat. Phys. 14 349 Google Scholar
[385]	He J, Chen D, Zhu W, Zhang S, Zhao L, Ren Z, Chen G 2017 Phys. Rev. B 95 195165 Google Scholar
[386]	Zhu W, He J, Zhang S, Chen D, Shan L, Ren Z, Chen G 2017 arXiv: 1707.00942 [cond-mat]
[387]	Kumar N, Sun Y, Nicklas M, Watzman S J, Young O, Leermakers I, Hornung J, Klotz J, Gooth J, Manna K 2019 Nat. Commun. 10 2475
[388]	Felser C, Yan B 2016 Nat. Mater. 15 1149 Google Scholar
[389]	Nayak A K, Fischer J E, Sun Y, Yan B, Karel J, Komarek A C, Shekhar C, Kumar N, Schnelle W, Kübler J 2016 Sci. Adv. 2 e1501870 Google Scholar
[390]	Wang Z, Vergniory M, Kushwaha S, Hirschberger M, Chulkov E, Ernst A, Ong N P, Cava R J, Bernevig B A 2016 Phys. Rev. Lett. 117 236401 Google Scholar
[391]	Chang G, Xu S Y, Zheng H, Singh B, Hsu C H, Bian G, Alidoust N, Belopolski I, Sanchez D S, Zhang S 2016 Sci. Rep. 6 38839
[392]	Nie S, Xu G, Prinz F B, Zhang S C 2017 Proc. Natl. Acad. Sci. 114 10596 Google Scholar
[393]	Yang H, Sun Y, Zhang Y, Shi W J, Parkin S S, Yan B 2017 New J. Phys. 19 015008 Google Scholar
[394]	Liu E, Sun Y, Kumar N, Muechler L, Sun A, Jiao L, Yang S Y, Liu D, Liang A, Xu Q 2018 Nat. Phys. 14 1125 Google Scholar
[395]	Wang Q, Xu Y, Lou R, Liu Z, Li M, Huang Y, Shen D, Weng H, Wang S, Lei H 2018 Nat. Commun. 9 3681
[396]	Guin S N, Manna K, Noky J, Watzman S J, Fu C, Kumar N, Schnelle W, Shekhar C, Sun Y, Gooth J 2019 NPG Asia Mater. 11 1 Google Scholar
[397]	Chang G, Singh B, Xu S Y, Bian G, Huang S M, Hsu C H, Belopolski I, Alidoust N, Sanchez D S, Zheng H 2018 Phys. Rev. B 97 041104 Google Scholar
[398]	Yin J X, Zhang S S, Li H, Jiang K, Chang G, Zhang B, Lian B, Xiang C, Belopolski I, Zheng H 2018 Nature 562 91 Google Scholar
[399]	Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A 2015 Nature 527 495 Google Scholar
[400]	Deng K, Wan G, Deng P, Zhang K, Ding S, Wang E, Yan M, Huang H, Zhang H, Xu Z 2016 Nat. Phys. 12 1105 Google Scholar
[401]	Jiang J, Liu Z, Sun Y, Yang H, Rajamathi C, Qi Y, Yang L, Chen C, Peng H, Hwang C 2017 Nat. Commun. 8 13973
[402]	Wang Y, Liu E, Liu H, Pan Y, Zhang L, Zeng J, Fu Y, Wang M, Xu K, Huang Z 2016 Nat. Commun. 7 13142
[403]	Zhang E, Chen R, Huang C, Yu J, Zhang K, Wang W, Liu S, Ling J, Wan X, Lu H Z 2017 Nano Lett. 17 878 Google Scholar
[404]	Chen D, Zhao L, He J, Liang H, Zhang S, Li C, Shan L, Wang S, Ren Z, Ren C 2016 Phys. Rev. B 94 174411 Google Scholar
[405]	Khim S, Koepernik K, Efremov D V, Klotz J, Förster T, Wosnitza J, Sturza M I, Wurmehl S, Hess C, van den Brink J 2016 Phys. Rev. B 94 165145 Google Scholar
[406]	Xu S Y, Alidoust N, Chang G, Lu H, Singh B, Belopolski I, Sanchez D S, Zhang X, Bian G, Zheng H 2017 Sci. Adv. 3 e1603266 Google Scholar
[407]	Belopolski I, Sanchez D S, Ishida Y, Pan X, Yu P, Xu S Y, Chang G, Chang T R, Zheng H, Alidoust N 2016 Nat. Commun. 7 13643
[408]	Chang G, Xu S Y, Sanchez D S, Huang S M, Lee C C, Chang T R, Bian G, Zheng H, Belopolski I, Alidoust N 2016 Sci. Adv. 2 e1600295 Google Scholar
[409]	Zhong C, Chen Y, Yu Z M, Xie Y, Wang H, Yang S A, Zhang S 2017 Nat. Commun. 8 15641 Google Scholar
[410]	Chen W, Lu H Z, Hou J M 2017 Phys. Rev. B 96 041102 Google Scholar
[411]	Yan Z, Bi R, Shen H, Lu L, Zhang S C, Wang Z 2017 Phys. Rev. B 96 041103 Google Scholar
[412]	Ezawa M 2017 Phys. Rev. B 96 041202 Google Scholar
[413]	Wang C, Lu H Z, Xie X 2020 Phys. Rev. B 102 041204 Google Scholar
[414]	Hu Y, Liu H, Jiang H, Xie X 2017 Phys. Rev. B 96 134201 Google Scholar
[415]	Wang L X, Li C Z, Yu D P, Liao Z M 2016 Nat. Commun. 7 10769 Google Scholar
[416]	Zheng H, Bian G, Chang G, Lu H, Xu S Y, Wang G, Chang T R, Zhang S, Belopolski I, Alidoust N 2016 Phys. Rev. Lett. 117 266804 Google Scholar
[417]	Zheng H, Zahid Hasan M 2018 Adv. Phys. X 3 1466661
[418]	Zheng H, Chang G, Huang S M, Guo C, Zhang X, Zhang S, Yin J, Xu S Y, Belopolski I, Alidoust N 2017 Phys. Rev. Lett. 119 196403 Google Scholar
[419]	Chang G, Xu S Y, Zheng H, Lee C C, Huang S M, Belopolski I, Sanchez D S, Bian G, Alidoust N, Chang T R 2016 Phys. Rev. Lett. 116 066601 Google Scholar
[420]	Wang S, Lin B C, Zheng W Z, Yu D, Liao Z M 2018 Phys. Rev. Lett. 120 257701 Google Scholar

施引文献

图 1 拓扑半金属的能带结构和贝里曲率　(a)拓扑半金属的能谱示意图, $ (k_x, k_y, k_z) $为波矢, $k_{/\!/}^2 = k_x^2+k_y^2$; (b)贝里曲率矢量场, 拓扑半金属的导带和价带在外尔点处接触, 且在该处存在一对单极子. 转载自文献 [56]

Fig. 1. The band structure and Berry curvature of the topological semimetal: (a) The energy spectrum of a topological semimetal,$ (k_x, k_y, k_z) $ is the wave vector, $k_{/\!/}^2 = k_x^2+k_y^2$; (b) the vector field of the Berry curvature. The conduction and valence bands of a topological semimetal touch at the Weyl nodes, and there is a pair of monopoles. Reproduced with permission from Ref. [56].

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图 2 在沿$ z $方向的磁场$ B $下, 外尔和狄拉克半金属的最小模型中沿$ k_{z} $色散的朗道能带. 转载自文献[74]

Fig. 2. The Landau energy bands along the $ k_{z} $ dispersion in the minimum model of Weyl and Dirac semimetals under the magnetic field $ B $ along the $ z $ direction. Reproduced with permission from Ref.[74].

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图 3 测量非线性霍尔效应的示意图. 转载自文献[82]

Fig. 3. Schematic of how to measure the nonlinear Hall effect. Reproduced with permission from Ref.[82].

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图 4 (a)半导体-超导体纳米线结构示意图^[172-177], 两端可能存在一对马约拉纳束缚态; (b)−(d)杂化能随着磁场变化的振荡曲线. 红色和黑色曲线为实验数据^[172], 蓝色为理论曲线. 转载自文献[84]

Fig. 4. (a) Schematic of the semiconductor-superconductor nanowire structure^[172-177], its two ends may host a pair of Majorana bound states; (b)−(d) oscillation curves of hybridization energy vary with magnetic field. The red and black curves are experimental data adapted from Ref. [172]. The blue curves are the theoritical results. Reproduced with permission from Ref.[84].

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图 5 在无序(虚线)和电子-电子相互作用(波浪线)下, 计算3D外尔半金属电导率的费曼图^{[71,72,191,196-199]}, 有向直线代表格林函数. 转载自文献 [73]

Fig. 5. In the disorder (dashed lines) and electron-electron interaction (wavy lines), the Feynman diagram^{[71,72,191,196-199]} of the conductivity of 3D Weyl semimetal, and the directed line represents the Green's function. Reproduced with permission from Ref [73].

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图 6 不同条件下的磁导$\delta\sigma^{\rm {qi}}(B)$对参数的依赖关系　(a) $\eta_{\rm I} = \eta_{*} = 0$ 时不同的相干长度$ l_{\phi} $; (b) $ \eta_{*} = 0 $时不同的$ \eta_{\rm I} $; (c)有限$ \eta_{*} $时不同的$ \eta_{\rm I} $; (d) $ \eta_{\rm I} $ 和 $ \eta_{*} $之间的差异, 其中$ \eta_{\rm I} $与能谷间散射相关, 而$ \eta_{*} $与能谷内散射相关. 虚线表示两个散射过程的相关性, $ \nu = \pm $是能谷指标. 转载自文献[73]

Fig. 6. The dependence of magnetoconductivity $ \delta\sigma^{\rm {qi}}(B) $ on parameters under different conditions: (a) Different coherence length $ l_{\phi} $ at $ \eta_{\rm I} = \eta_{*} = 0 $; (b) different $ \eta_{\rm I} $ at $ \eta_{*} = 0 $; (c) different $ \eta_{\rm I} $ at finite $ \eta_{*} $; (d) the difference between $ \eta_{\rm I} $ and $ \eta_{*} $, where $ \eta_{\rm I} $ is correlated with intervalley scattering and $ \eta_{*} $ is correlated with intravalley scattering. The dashed lines indicate the correlation between the two scattering processes. $ \nu = \pm $ is the valley index. Reproduced with permission from Ref.[73].

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图 7 3D拓扑半金属动量空间中的费米球, 其中位于原点的点表示单极子荷$ {\cal{N}} $　(a) $ P $表示从波矢$ {{k}} $到标记为(${{k}}_1, {{k}}_2, \cdots, {{k}}_n$)的中间态的背散射, $ P' $ 表示$ P $的时间反演; (b) $ P $ 和$ P' $ 之间的相位差等效于在环路 $ {\cal{C}} = P+\bar{P} $周围累计的贝里相位. 转载自文献 [75]

Fig. 7. The Fermi sphere in 3D topological semimetal momentum space, where the dot at the origin represents monopole charge $ {\cal{N}} $: (a) $ P $ is the backscattering from the wave vector $ {{k}} $ to $ -{{k}} $ via intermediate states labeled as (${{k}}_1, {{k}}_2, \cdots, {{k}}_n$), $ P' $ represents the time-reversal of $ P $; (b) the phase difference between $ P $ and $ P' $ is equivalent to the Berry phase accumulated around loop $ {\cal{C}} = P+\bar{P} $. Reproduced with permission from Ref. [75].

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图 8 电导率$ \Delta\sigma $随温度$ T $变化的示意图. 选择$ c_{\rm {ee}} = c_{\rm {qi}} $, $ T_{\rm c} $是电导率随温度降低而下降的临界温度. 转载自文献 [73]

Fig. 8. The schematic diagram of conductivity $ \Delta\sigma $ changes with temperature $ T $. We choose $ c_{\rm {ee}} = c_{\rm {qi}} $, $ T_{\rm c} $ is the critical temperature at which the conductivity drops with temperature. Reproduced with permission from Ref. [73].

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图 9 (a)节线半金属的轮胎状费米面, 小半径$ \kappa $, 主半径$ k_0 $, 极向角$ \varphi $, 环面角$ \theta $; (b)对于短程杂质势导致在环形方向上产生从$ { k} $到$ -{ k} $ 的相干背散射; (c)在长程杂质势作用下, 沿极向的$ \delta { k} $到$ -\delta { k} $的散射, 此过程积累一个大小为$ \pi $的贝里相位. 转载自文献[147]

Fig. 9. (a) Torus-shaped Fermi surface of nodal-line semimetals, with minor radius$ \kappa $, major radius$ k_0 $, poloidal angle$ \varphi $, and toroidal angle $ \theta $; (b) a coherent backscattering from wave vector $ { k} $ to $ -{ k} $ around the toroidal direction for shortranged impurity potentials; (c) backscattering from wave vector$ \delta { k} $ to $ -\delta { k} $ along the poloidal direction under long-ranged impurity potentials.The process contributs a $ \pi $ Berry phase. Reproduced with permission from Ref.[147].

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图 10 不同相位相干长度$ l_\phi $下的磁导率, 短程极限(a)和长程极限(b)分别对应(33)式和(34)式. 转载自文献[147]

Fig. 10. The magnetoconductivity in the (a) short range limit Eq. (33) and (b) long range limit Eq.(34) for different phase coherence lengths $ l_\phi $. Reproduced with permission from Ref.[147].

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图 11 (a)磁导率 $ \delta\sigma\equiv\sigma(B)-\sigma(0) $与磁场$ B $的关系; (b) 电导率$ \sigma $ 与温度$ T $的关系. 转载自文献[72]

Fig. 11. The magnetoconductivity $ \delta\sigma\equiv\sigma(B)-\sigma(0) $; (b) conductivity $ \sigma $ vs temperature $ T $. Reproduced with permission from Ref. [72].

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图 12 理论计算的负磁阻与实验^[152-154]的比较. 转载自文献[80]

Fig. 12. The comparison between the theoretical negative magnetoresistance and the experiments^[152-154]. Reproduced with permission from Ref. [80].

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图 13 对于(1)式描述的外尔半金属, 数值(散点)和解析(实线)得到的频率$ F $的曲线　(a)固定$ M $对应不同的$ A $; (b)固定$ A $对应不同的$ M $. (c)固定$ E_M $ 不同的$ E_A $ 对应的相移$ \phi $的曲线. 曲线断裂是因为在拍频模式出现时, F和$ \phi $无法拟合. 垂直虚线表示栗弗席兹点. 转载自文献[77]

Fig. 13. For the Weyl semimetal described in Eq. (1), the frequency $ F $ obtained by numerical (scatters) and analytical (solid curves): (a) Fixed $ M $ corresponds to different $ A $; (b) fixed $ A $ corresponds to different $ M $. (c) Fixed $ E_M $, for different $ E_A $ corresponds to the curve of phase shift $ \phi $. The curve breaks because $ F $ and $ \phi $ can not fit when beating patterns occur. The vertical dashed lines represents the Lifshitz point. Reproduced with permission from Ref.[77].

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图 14 (a) (17)式中节线半金属的节线(虚线环), 轮胎状和鼓形费米面, $ E_{\rm F} $是费米能, $ u $ 是模型参数; (b)轮胎状费米面在节线平面内的最大($ \alpha $)和最小($ \beta $)截面; (c)轮胎状费米面在节线平面外的最大($ \gamma $)和最小($ \delta $)截面. 转载自文献[79]

Fig. 14. (a) In the model of nodal-line semimetal Eq.(17), the nodal line (dashed ring), torus and drum Fermi surface, $ E_{\rm F} $ is Fermi energy, $ u $ is model parameter; (b) the maximum ($ \alpha $) and minimum ($ \beta $) cross sections of the torus Fermi surface; (c) the maximum ($ \gamma $) and minimum ($ \delta $) cross sections of the Fermi surface outside the nodal-line plane. Reproduced with permission from Ref. [79].

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图 15 (a)外尔半金属中的费米弧和体态的色散, $ k_{/\!/} $表示$ (k_x, k_y) $; (b)在$k_z\text-k_x$平面上$ y = L/2 $, $ E_{\rm F} = E_w $处的费米弧; (c)宽度为$ W $, 厚度为$ L $的外尔半金属板; (d)在$E_{\rm F} = E_w$处的费米弧(实线); (e)−(g)波函数在$ k_z = 0 $处沿$ y $轴的分布; (h) 3D量子霍尔效应中的朗道能级和边缘态; (i)单一表面的电子无法被y方向的磁场$ B $驱动完成一个完整的回旋运动. 转载自文献[78,283]

Fig. 15. (a) The energy dispersions of the Fermi arc and bulk states in a Weyl semimetal, $ k_{/\!/} $ stands for $ (k_x, k_y) $; (b) the Fermi arc at $ y = L/2 $ and $ E_{\rm F} = E_w $ in the $ k_z\text-k_x $ plane; (c) a Weyl semimetal slab with width $ W $ and thickness $ L $; (d) Fermi arc (solid) at $ E_{\rm F} = E_w $; (e)−(g) the distribution of wave function along $ y $-axis at $ k_z = 0 $; (h) the Landau levels and edge states in the 3D quantum Hall effect; (i) an electron in single surface could not be driven in a y-direction magnetic field $ B $ to perform a complete cyclotron motion. Reproduced with permission from Refs. [78,283].

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图 16 左图: 2D电子气在磁场中形成量子霍尔态. 中间图: 3D时朗道能级变为一系列2D的朗道能带. 右图:电荷密度波使朗道能带打开能隙, 使体态绝缘, 可以观察到3D量子霍尔效应. 转载自文献[87]

Fig. 16. Left: the quantum Hall state in 2D electron gas under magnetic field. Center: in 3D, the Landau levels turn to one dimensional Landau bands. Right: the charge density wave gap the Landau band, so that the bulk is insulating and the 3D quantum Hall effect can be observed. Reproduced with permission from Ref. [87].

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图 17 不同的势范围下, 外尔半金属在$ \hat{{z}} $方向磁场B中的纵向电导率$ \sigma_{zz} $和横向电导率$ \sigma_{xx} $. 转载自文献[76]

Fig. 17. The longitudinal conductivity $ \sigma_{zz} $ and transverse conductivity $ \sigma_{xx} $ of the Weyl semimetal in the $ \hat{{z}} $-direction magnetic field B under the different potential ranges. Reproduced with permission from Ref. [76].

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图 18 (a) 3D拓扑绝缘体的零场能谱($ k_x = k_y = 0 $); (b)在强磁场中, 费米能只穿过$ 0+ $朗道能带; (c)实验测得Pb_1–xSn_xSe的磁阻^[226]; (d)理论计算出的磁阻. 转载自文献[81]

Fig. 18. (a) The zero field energy spectrum of 3D topological insulator ($ k_x = k_y = 0 $); (b) in a strong magnetic field, fermi energy $ E_{\rm F} $ can only crosses the $ 0+ $ Landau energy band; (c) the magnetoresistance of Pb_1–xSn_xSe in experiment^[226]; (d) the theoretical calculated magnetoresistance. Reproduced with permission from Ref. [81].

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图 19 外尔半金属在垂直$ y $方向的磁场$ {{B}} $中的朗道能带, 其中$ k_{/\!/}\equiv k_x\sin\phi+k_z\cos\phi $为平行于$ {{B}} $的波矢, $\tan\phi = B_x/B_z$. 红色曲线是第0个朗道能带, 虚线是费米能. 转载自文献[70]

Fig. 19. The Landau energy band of Weyl semimetal in the magnetic field $ {{B}} $ perpendicular to the $ y $ direction, where $ k_{/\!/}\equiv k_x\sin\phi+k_z\cos\phi $ is the wave vector parallel to $ {{B}} $, $ \tan\phi = B_x/B_z $. The red curve is the $ 0 $th Landau energy band, and the dashed line represents the Fermi energy. Reproduced with permission from Ref. [70].

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图 20 实验与理论的比较　(a) $M_{/\!/}$(黑线); (b)$ M_{\rm T} $(黑线). 转载自文献[85]

Fig. 20. Comparison between experiments and theory for the $M_{/\!/}$ and $ M_{\rm T} $ of TaAs: (a) $M_{/\!/}$(black line); (b) $ M_{\rm T} $(black line). Reproduced with permission from Ref. [85].

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图 21 零磁场下ZrTe₅的电阻率$ \rho(T) $(黑色)和塞贝克系数$ –S_{x x}(T) $(蓝色)的温度依赖曲线. 插图:实验测量示意图, $ B $是磁场, $ \nabla T $是温度梯度, $ a $, $ b $和$ c $是晶轴. 转载自文献[86]

Fig. 21. Temperature dependence of the electrical resistivity $ \rho(T) $ (black) and Seebeck coefficient $ –S_{x x}(T) $ (blue) of ZrTe$ _5 $ at zero magnetic field. Inset: the measurement setup. $ B $ is the magnetic field and $ \nabla T $ is the temperature gradient. $ a, b$ and $c$ are crystallographic axes. Reproduced with permission from Ref. [86].

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图 22 (a)不同温度下对$ –S_{x x} $的强场测量; (b)不同温度下对 $ S_{xy} $的强场测量. 临界场$ B^{*} $附近$ S_{xy} $改变符号, $ –S_{x x} $收敛到零. 转载自文献[86]

Fig. 22. (a) High-field measurements of $ –S_{x x} $ at several temperatures; (b) high-field measurements of $ S_{xy} $ at several temperatures. Near the critical field $ B^{*} $, $ S_{xy} $ changes its sign and $ –S_{x x} $ converges to zero. Reproduced with permission from Ref. [86].

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表 1 对称类(正交、辛和幺正)^[194]与弱局域化(WL)和弱反局域化(WAL)之间的关系^[195]. 转载自文献 [88]

Table 1. The relation between the symmetry classes (orthogonal, symplectic and unitary) ^[194] and weak localization (WL) and anti-localization (WAL) ^[195]. Reproduced with permission from Ref. [88].

	正交	辛	幺正
时间反演	√	√	×
自旋旋转	√	×	×
WL/WAL	WL	WAL	×

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表 2 对于具有不同色散和维度的系统, (48)式中的相移$\phi$. $B_z$和$B_{/\!/}$是节线平面内外的磁场. $\alpha$, $\beta$, $\gamma$, δ 对应于图14中费米面的截面. 转载自文献[79]

Table 2. For systems with different dispersion and dimensions, the phase shift ϕ in Eq. (48). $B_z$ and $B_{/\!/}$ are magnetic fields outside and inside the nodal-line plane. $\alpha$, $\beta$, $\gamma$, and $\delta$ correspond to the cross sections of Fermi surface in Fig. 14. Reproduced with permission from Ref. [79].

系统	电子载流子	空穴载流子
2D抛物线	–1/2	1/2
3D抛物线	–5/8	5/8
2D线性	0	0
3D线性	–1/8	1/8
磁场$B_z$中的节线	$-5/8(\alpha), 5/8(\beta)$	$5/8(\alpha), -5/8(\beta)$
磁场$B_{/\!/}$中的节线	$-5/8(\gamma), 1/8(\delta)$	$5/8(\gamma), -1/8(\delta)$

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表 3 从Cd₃As₂的实验中得到的相移$\phi_{\exp}$. 转载自文献[77]

Table 3. The phase shift $\phi_{\exp}$ obtained from the experiment of Cd₃As₂. Reproduced with permission from Ref. [77].

文献	$\phi_{\rm{exp}}$	$\phi_{\rm{Weyl}}$	$\phi_{\rm{Dirac}}$
[50]	0.06 — 0.08	–0.94 — –0.92	–5/8
[51]	0.11 — 0.38	–0.89 — –0.62	–5/8
[54]	0.04	–0.96	–5/8

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表 4 节线半金属的相移$\phi$. $\alpha, \beta, \gamma, \delta$ 是图14中的极值截面. 转载自文献[79]

Table 4. The phase shift $\phi$ of the nodal-line semimetal. $\alpha, \beta, \gamma, \delta$ are the extremal cross sections in Fig. 14. Reproduced with permission from Ref. [79].

	贝里相位	最大/ 最小	电子	空穴
$\alpha$	0	最大	$ -1/2+0-1/8 = -5/8 $	+5/8
$\beta$	0	最小	$-1/2+0+1/8 = -3/8 \leftrightarrow 5/8$	–5/8
$\gamma$	0	最大	$ -1/2+0 - 1/8 = - 5/8 $	+5/8
δ	π	最小	$-1/2+\pi/2\pi+1/8 = 1/8$	–1/8

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[1]	Balents L 2011 Physics 4 36 Google Scholar
[2]	Volovik G E 2003 The Universe in a Helium Droplet (Vol. 117) (New York: Oxford University Press) pp32−41
[3]	Wan X, Turner A M, Vishwanath A, Savrasov S Y 2011 Phys. Rev. B 83 205101 Google Scholar
[4]	Yang K Y, Lu Y M, Ran Y 2011 Phys. Rev. B 84 075129 Google Scholar
[5]	Burkov A, Balents L 2011 Phys. Rev. Lett. 107 127205 Google Scholar
[6]	Xu G, Weng H, Wang Z, Dai X, Fang Z 2011 Phys. Rev. Lett. 107 186806 Google Scholar
[7]	Jiang J H 2012 Phys. Rev. A 85 033640 Google Scholar
[8]	Young S M, Zaheer S, Teo J C, Kane C L, Mele E J, Rappe A M 2012 Phys. Rev. Lett. 108 140405 Google Scholar
[9]	Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X, Fang Z 2012 Phys. Rev. B 85 195320 Google Scholar
[10]	Singh B, Sharma A, Lin H, Hasan M, Prasad R, Bansil A 2012 Phys. Rev. B 86 115208 Google Scholar
[11]	Wang Z, Weng H, Wu Q, Dai X, Fang Z 2013 Phys. Rev. B 88 125427 Google Scholar
[12]	Liu J, Vanderbilt D 2014 Phys. Rev. B 90 155316 Google Scholar
[13]	Bulmash D, Liu C X, Qi X L 2014 Phys. Rev. B 89 081106 Google Scholar
[14]	Brahlek M, Bansal N, Koirala N, Xu S Y, Neupane M, Liu C, Hasan M Z, Oh S 2012 Phys. Rev. Lett. 109 186403 Google Scholar
[15]	Wu L, Brahlek M, Aguilar R V, Stier A, Morris C, Lubashevsky Y, Bilbro L, Bansal N, Oh S, Armitage N 2013 Nat. Phys. 9 410 Google Scholar
[16]	Liu Z, Zhou B, Zhang Y, Wang Z, Weng H, Prabhakaran D, Mo S K, Shen Z, Fang Z, Dai X 2014 Science 343 864 Google Scholar
[17]	Xu S Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C C 2015 Science 349 613 Google Scholar
[18]	Liu Z, Jiang J, Zhou B, Wang Z, Zhang Y, Weng H, Prabhakaran D, Mo S K, Peng H, Dudin P 2014 Nat. Mater. 13 677 Google Scholar
[19]	Neupane M, Xu S Y, Sankar R, Alidoust N, Bian G, Liu C, Belopolski I, Chang T R, Jeng H T, Lin H 2014 Nat. Commun. 5 3786
[20]	Yi H, Wang Z, Chen C, Shi Y, Feng Y, Liang A, Xie Z, He S, He J, Peng Y 2014 Sci. Rep. 4 6106
[21]	Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava R J 2014 Phys. Rev. Lett. 113 027603 Google Scholar
[22]	Weng H, Fang C, Fang Z, Bernevig B A, Dai X 2015 Phys. Rev. X 5 011029
[23]	Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B, Alidoust N, Bian G, Neupane M, Zhang C 2015 Nat. Commun. 6 7373
[24]	Lv B, Weng H, Fu B, Wang X P, Miao H, Ma J, Richard P, Huang X, Zhao L, Chen G, et al. 2015 Phys. Rev. X 5 031013
[25]	Borisenko S, Evtushinsky D, Gibson Q, Yaresko A, Koepernik K, Kim T, Ali M, van den Brink J, Hoesch M, Fedorov A 2019 Nat. Commun. 10 3424 Google Scholar
[26]	Nielsen H B, Ninomiya M 1981 Nucl. Phys. B 185 20 Google Scholar
[27]	Nielsen H B, Ninomiya M 1983 Phys. Lett. B 130 389 Google Scholar
[28]	Son D, Spivak B 2013 Phys. Rev. B 88 104412 Google Scholar
[29]	Burkov A 2014 Phys. Rev. Lett. 113 247203 Google Scholar
[30]	Kharzeev D E, Yee H U 2013 Phys. Rev. B 88 115119 Google Scholar
[31]	Parameswaran S, Grover T, Abanin D, Pesin D, Vishwanath A 2014 Phys. Rev. X 4 031035
[32]	Zhou J, Chang H R, Xiao D 2015 Phys. Rev. B 91 035114 Google Scholar
[33]	Son D T, Yamamoto N 2012 Phys. Rev. Lett. 109 181602 Google Scholar
[34]	Stephanov M, Yin Y 2012 Phys. Rev. Lett. 109 162001 Google Scholar
[35]	Landsteiner K, Megias E, Pena-Benitez F 2011 Phys. Rev. Lett. 107 021601 Google Scholar
[36]	Chang M C, Yang M F 2015 Phys. Rev. B 91 115203 Google Scholar
[37]	Jiang Q D, Jiang H, Liu H, Sun Q F, Xie X 2015 Phys. Rev. Lett. 115 156602 Google Scholar
[38]	Jiang Q D, Jiang H, Liu H, Sun Q F, Xie X 2016 Phys. Rev. B 93 195165 Google Scholar
[39]	Chen C Z, Song J, Jiang H, Sun Q f, Wang Z, Xie X 2015 Phys. Rev. Lett. 115 246603 Google Scholar
[40]	Chen C Z, Liu H, Jiang H, Xie X 2016 Phys. Rev. B 93 165420 Google Scholar
[41]	Kim H J, Kim K S, Wang J F, Sasaki M, Satoh N, Ohnishi A, Kitaura M, Yang M, Li L 2013 Phys. Rev. Lett. 111 246603 Google Scholar
[42]	Kim K S, Kim H J, Sasaki M 2014 Phys. Rev. B 89 195137 Google Scholar
[43]	Li Q, Kharzeev D E, Zhang C, Huang Y, Pletikosić I, Fedorov A, Zhong R, Schneeloch J, Gu G, Valla T 2016 Nat. Phys. 12 550 Google Scholar
[44]	Chen R, Chen Z, Song X Y, Schneeloch J, Gu G, Wang F, Wang N 2015 Phys. Rev. Lett. 115 176404 Google Scholar
[45]	Zheng G, Lu J, Zhu X, Ning W, Han Y, Zhang H, Zhang J, Xi C, Yang J, Du H, et al. 2016 Phys. Rev. B 93 115414 Google Scholar
[46]	Xiong J, Kushwaha S K, Liang T, Krizan J W, Hirschberger M, Wang W, Cava R J, Ong N P 2015 Science 350 413 Google Scholar
[47]	Jeon S, Zhou B B, Gyenis A, Feldman B E, Kimchi I, Potter A C, Gibson Q D, Cava R J, Vishwanath A, Yazdani A 2014 Nat. Mater. 13 851 Google Scholar
[48]	Liang T, Gibson Q, Ali M N, Liu M, Cava R, Ong N 2015 Nat. Mater. 14 280 Google Scholar
[49]	Feng J, Pang Y, Wu D, Wang Z, Weng H, Li J, Dai X, Fang Z, Shi Y, Lu L 2015 Phys. Rev. B 92 081306 Google Scholar
[50]	He L, Hong X, Dong J, Pan J, Zhang Z, Zhang J, Li S 2014 Phys. Rev. Lett. 113 246402 Google Scholar
[51]	Zhao Y, Liu H, Zhang C, Wang H, Wang J, Lin Z, Xing Y, Lu H, Liu J, Wang Y, et al. 2015 Phys. Rev. X 5 031037
[52]	Cao J, Liang S, Zhang C, Liu Y, Huang J, Jin Z, Chen Z G, Wang Z, Wang Q, Zhao J 2015 Nat. Commun. 6 7779
[53]	Shekhar C, Nayak A K, Sun Y, Schmidt M, Nicklas M, Leermakers I, Zeitler U, Skourski Y, Wosnitza J, Liu Z 2015 Nat. Phys. 11 645 Google Scholar
[54]	Narayanan A, Watson M, Blake S, Bruyant N, Drigo L, Chen Y, Prabhakaran D, Yan B, Felser C, Kong T 2015 Phys. Rev. Lett. 114 117201 Google Scholar
[55]	Li C Z, Wang L X, Liu H, Wang J, Liao Z M, Yu D P 2015 Nat. Commun. 6 10137
[56]	Li H, He H, Lu H Z, Zhang H, Liu H, Ma R, Fan Z, Shen S Q, Wang J 2016 Nat. Commun. 7 10301
[57]	Zhang C, Zhang E, Liu Y, Chen Z G, Liang S, Cao J, Yuan X, Tang L, Li Q, Gu T, et al. 2015 arXiv: 1504.07698 [cond-mat]
[58]	Wang H, Wang H, Liu H, Lu H, Yang W, Jia S, Liu X J, Xie X, Wei J, Wang J 2016 Nat. Mater. 15 38 Google Scholar
[59]	Aggarwal L, Gaurav A, Thakur G S, Haque Z, Ganguli A K, Sheet G 2016 Nat. Mater. 15 32 Google Scholar
[60]	Huang X, Zhao L, Long Y, Wang P, Chen D, Yang Z, Liang H, Xue M, Weng H, Fang Z 2015 Phys. Rev. X 5 031023
[61]	Zhang C L, Xu S Y, Belopolski I, Yuan Z, Lin Z, Tong B, Bian G, Alidoust N, Lee C C, Huang S M 2016 Nat. Commun. 7 10735
[62]	Zhang C, Guo C, Lu H, Zhang X, Yuan Z, Lin Z, Wang J, Jia S 2015 Phys. Rev. B 92 041203 Google Scholar
[63]	Arnold F, Shekhar C, Wu S C, Sun Y, Dos Reis R D, Kumar N, Naumann M, Ajeesh M O, Schmidt M, Grushin A G 2016 Nat. Commun. 7 11615
[64]	Zhang C L, Xu S Y, Wang C, Lin Z, Du Z, Guo C, Lee C C, Lu H, Feng Y, Huang S M 2017 Nat. Phys. 13 979 Google Scholar
[65]	Yang X, Liu Y, Wang Z, Zheng Y, Xu Z A 2015 arXiv: 1506.03190 [cond-mat]
[66]	Li Y, Wang Z, Li P, Yang X, Shen Z, Sheng F, Li X, Lu Y, Zheng Y, Xu Z A 2017 Front. Phys. 12 127205 Google Scholar
[67]	Wang Z, Zheng Y, Shen Z, Lu Y, Fang H, Sheng F, Zhou Y, Yang X, Li Y, Feng C, et al. 2016 Phys. Rev. B 93 121112 Google Scholar
[68]	Wang H, Li C K, Liu H, Yan J, Wang J, Liu J, Lin Z, Li Y, Wang Y, Li L 2016 Phys. Rev. B 93 165127 Google Scholar
[69]	Lu H Z, Shen S Q 2017 Front. Phys. 12 127201 Google Scholar
[70]	Sun H P, Lu H Z 2019 Front. Phys. 14 33405 Google Scholar
[71]	Lu H Z, Shi J, Shen S Q 2011 Phys. Rev. Lett. 107 076801 Google Scholar
[72]	Lu H Z, Shen S Q 2014 Phys. Rev. Lett. 112 146601 Google Scholar
[73]	Lu H Z, Shen S Q 2015 Phys. Rev. B 92 035203 Google Scholar
[74]	Lu H Z, Zhang S B, Shen S Q 2015 Phys. Rev. B 92 045203 Google Scholar
[75]	Dai X, Lu H Z, Shen S Q, Yao H 2016 Phys. Rev. B 93 161110 Google Scholar
[76]	Zhang S B, Lu H Z, Shen S Q 2016 New J. Phys. 18 053039 Google Scholar
[77]	Wang C, Lu H Z, Shen S Q 2016 Phys. Rev. Lett. 117 077201 Google Scholar
[78]	Wang C, Sun H P, Lu H Z, Xie X 2017 Phys. Rev. Lett. 119 136806 Google Scholar
[79]	Li C, Wang C, Wan B, Wan X, Lu H Z, Xie X 2018 Phys. Rev. Lett. 120 146602 Google Scholar
[80]	Dai X, Du Z, Lu H Z 2017 Phys. Rev. Lett. 119 166601 Google Scholar
[81]	Chen Y, Lu H Z, Xie X 2018 Phys. Rev. Lett. 121 036602 Google Scholar
[82]	Du Z, Wang C, Lu H Z, Xie X 2018 Phys. Rev. Lett. 121 266601 Google Scholar
[83]	Du Z, Wang C, Li S, Lu H Z, Xie X 2019 Nat. Commun. 10 3047
[84]	Cao Z, Zhang H, Lü H F, He W X, Lu H Z, Xie X 2019 Phys. Rev. Lett. 122 147701 Google Scholar
[85]	Zhang C L, Wang C, Yuan Z, Xu X, Wang G, Lee C C, Pi L, Xi C, Lin H, Harrison N 2019 Nat. Commun. 10 1028
[86]	Zhang J, Wang C, Guo C, et al. 2018 Phys. Rev. Lett. 123 196602
[87]	Qin Fang, Li Shuai, Du Z Z, Wang C M, Zhang W Q, Yu D P, Lu H Z, Xie X C 2020 Phys. Rev. Lett. 125 206601 Google Scholar
[88]	Lu H Z, Shen S Q 2016 Chin. Phys. B 25 117202 Google Scholar
[89]	Hosur P, Qi X 2013 C. R. Phys. 14 857 Google Scholar
[90]	Weng H, Dai X, Fang Z 2016 J. Phys. Condes. Matter 28 303001 Google Scholar
[91]	Yan B, Felser C 2017 Annu. Rev. Condens. Matter Phys. 8 337 Google Scholar
[92]	Armitage N, Mele E, Vishwanath A 2018 Rev. Mod. Phys. 90 015001 Google Scholar
[93]	Wang H, Wang J 2018 Chin. Phys. B 27 107402 Google Scholar
[94]	Shen S Q 2017 Topological Insulators: Dirac Equation in Condensed Matter (Vol. 187) (Singapore: Springer) pp207−229
[95]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[96]	Asbóth J K, Oroszlány L, Pályi A P 2016 A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions (Vol. 919) (Heidelberg, New York, London: Springer) p33
[97]	Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B 81 115407 Google Scholar
[98]	Shan W Y, Lu H Z, Shen S Q 2010 New J. Phys. 12 043048 Google Scholar
[99]	Shen S Q, Shan W Y, Lu H Z 2011 Spin 01 33 Google Scholar
[100]	Shen S Q, Ma M, Xie X, Zhang F C 2004 Phys. Rev. Lett. 92 256603 Google Scholar
[101]	Shen S Q, Bao Y J, Ma M, Xie X, Zhang F C 2005 Phys. Rev. B 71 155316 Google Scholar
[102]	Sakurai J, Napolitano J 2017 Modern Quantum Mechanics (Cambridge: Cambridge University Press) pp105−108
[103]	Yang L, Liu Z, Sun Y, Peng H, Yang H, Zhang T, Zhou B, Zhang Y, Guo Y, Rahn M, et al. 2015 Nat. Phys. 11 728 Google Scholar
[104]	Xu S Y, Alidoust N, Belopolski I, Yuan Z, Bian G, Chang T R, Zheng H, Strocov V N, Sanchez D S, Chang G 2015 Nat. Phys. 11 748 Google Scholar
[105]	Xu N, Weng H, Lv B, Matt C E, Park J, Bisti F, Strocov V N, Gawryluk D, Pomjakushina E, Conder K 2016 Nat. Commun. 7 11006
[106]	Guan T, Lin C, Yang C, Shi Y, Ren C, Li Y, Weng H, Dai X, Fang Z, Yan S 2015 Phys. Rev. Lett. 115 087002 Google Scholar
[107]	Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Chang T R, Wang B, Alidoust N, Bian G, Neupane M 2016 Proc. Natl. Acad. Sci. 113 1180 Google Scholar
[108]	Burkov A, Hook M, Balents L 2011 Phys. Rev. B 84 235126 Google Scholar
[109]	Chiu C K, Schnyder A P 2014 Phys. Rev. B 90 205136 Google Scholar
[110]	Fang C, Weng H, Dai X, Fang Z 2016 Chin. Phys. B 25 117106 Google Scholar
[111]	Yang B J, Bojesen T A, Morimoto T, Furusaki A 2017 Phys. Rev. B 95 075135 Google Scholar
[112]	Chen Y, Xie Y, Yang S A, Pan H, Zhang F, Cohen M L, Zhang S 2015 Nano Lett. 15 6974 Google Scholar
[113]	Bzdušek T, Wu Q, Rüegg A, Sigrist M, Soluyanov A A 2016 Nature 538 75 Google Scholar
[114]	Feng X, Yue C, Song Z, Wu Q, Wen B 2018 Phys. Rev. Mater. 2 014202 Google Scholar
[115]	Yi C J, Lv B, Wu Q, Fu B B, Gao X, Yang M, Peng X L, Li M, Huang Y B, Richard P 2018 Phys. Rev. B 97 201107 Google Scholar
[116]	Chen W, Luo K, Li L, Zilberberg O 2018 Phys. Rev. Lett. 121 166802 Google Scholar
[117]	Zhu Z, Chang T R, Huang C Y, Pan H, Nie X A, Wang X Z, Jin Z T, Xu S Y, Huang S M, Guan D D 2018 Nat. Commun. 9 4153
[118]	Chen W, Lado J L 2019 Phys. Rev. Lett. 122 016803 Google Scholar
[119]	Weng H, Liang Y, Xu Q, Yu R, Fang Z, Dai X, Kawazoe Y 2015 Phys. Rev. B 92 045108 Google Scholar
[120]	Yu R, Weng H, Fang Z, Dai X, Hu X 2015 Phys. Rev. Lett. 115 036807 Google Scholar
[121]	Kim Y, Wieder B J, Kane C, Rappe A M 2015 Phys. Rev. Lett. 115 036806 Google Scholar
[122]	Fang C, Chen Y, Kee H Y, Fu L 2015 Phys. Rev. B 92 081201 Google Scholar
[123]	Chen Y, Lu Y M, Kee H Y 2015 Nat. Commun. 6 6593
[124]	Bian G, Chang T R, Zheng H, Velury S, Xu S Y, Neupert T, Chiu C K, Huang S M, Sanchez D S, Belopolski I 2016 Phys. Rev. B 93 121113 Google Scholar
[125]	Xie L S, Schoop L M, Seibel E M, Gibson Q D, Xie W, Cava R J 2015 APL Mater. 3 083602 Google Scholar
[126]	Chan Y H, Chiu C K, Chou M, Schnyder A P 2016 Phys. Rev. B 93 205132 Google Scholar
[127]	Du Y, Tang F, Wang D, Sheng L, Kan E j, Duan C G, Savrasov S Y, Wan X 2017 npj Quantum Mater. 2 1 Google Scholar
[128]	Zhao J, Yu R, Weng H, Fang Z 2016 Phys. Rev. B 94 195104 Google Scholar
[129]	Yamakage A, Yamakawa Y, Tanaka Y, Okamoto Y 2016 J. Phys. Soc. Jpn. 85 013708 Google Scholar
[130]	Xu Q, Yu R, Fang Z, Dai X, Weng H 2017 Phys. Rev. B 95 045136 Google Scholar
[131]	Jin Y J, Wang R, Zhao J Z, Du Y P, Zheng C D, Gan L Y, Liu J F, Xu H, Tong S 2017 Nanoscale 9 13112 Google Scholar
[132]	Zhu Z, Li M, Li J 2016 Phys. Rev. B 94 155121 Google Scholar
[133]	Liang Q F, Zhou J, Yu R, Wang Z, Weng H 2016 Phys. Rev. B 93 085427 Google Scholar
[134]	Zeng M, Fang C, Chang G, Chen Y A, Hsieh T, Bansil A, Lin H, Fu L 2015 arXiv: 1504.03492 [cond-mat]
[135]	Hirayama M, Okugawa R, Miyake T, Murakami S 2017 Nat. Commun. 8 14022
[136]	Huang H, Liu J, Vanderbilt D, Duan W 2016 Phys. Rev. B 93 201114 Google Scholar
[137]	Li R, Ma H, Cheng X, Wang S, Li D, Zhang Z, Li Y, Chen X Q 2016 Phys. Rev. Lett. 117 096401 Google Scholar
[138]	Wang J T, Weng H, Nie S, Fang Z, Kawazoe Y, Chen C 2016 Phys. Rev. Lett. 116 195501 Google Scholar
[139]	Sun Y, Zhang Y, Liu C X, Felser C, Yan B 2017 Phys. Rev. B 95 235104 Google Scholar
[140]	Schoop L M, Ali M N, Straßer C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S, Lotsch B V, Ast C R 2016 Nat. Commun. 7 11696
[141]	Neupane M, Belopolski I, Hosen M M, Sanchez D S, Sankar R, Szlawska M, Xu S Y, Dimitri K, Dhakal N, Maldonado P 2016 Phys. Rev. B 93 201104 Google Scholar
[142]	Chen C, Xu X, Jiang J, Wu S C, Qi Y, Yang L, Wang M, Sun Y, Schröter N, Yang H 2017 Phys. Rev. B 95 125126 Google Scholar
[143]	Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I 2016 Nat. Commun. 7 10556
[144]	Chang T R, Chen P J, Bian G, Huang S M, Zheng H, Neupert T, Sankar R, Xu S Y, Belopolski I, Chang G 2016 Phys. Rev. B 93 245130 Google Scholar
[145]	Ekahana S A, Wu S C, Jiang J, Okawa K, Prabhakaran D, Hwang C C, Mo S K, Sasagawa T, Felser C, Yan B 2017 New J. Phys. 19 065007 Google Scholar
[146]	Wu Y, Wang L L, Mun E, Johnson D D, Mou D, Huang L, Lee Y, Bud’ko S L, Canfield P C, Kaminski A 2016 Nat. Phys. 12 667 Google Scholar
[147]	Chen W, Lu H Z, Zilberberg O 2019 Phys. Rev. Lett. 122 196603 Google Scholar
[148]	Alexandradinata A, Glazman L 2018 Phys. Rev. B 97 144422 Google Scholar
[149]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[150]	Nechaev I, Krasovskii E 2016 Phys. Rev. B 94 201410 Google Scholar
[151]	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 2010 Nat. Phys. 6 584 Google Scholar
[152]	Wang J, Li H, Chang C, He K, Lee J S, Lu H, Sun Y, Ma X, Samarth N, Shen S 2012 Nano Res. 5 739 Google Scholar
[153]	He H, Liu H, Li B, Guo X, Xu Z, Xie M, Wang J 2013 Appl. Phys. Lett. 103 031606 Google Scholar
[154]	Wiedmann S, Jost A, Fauqué B, Van Dijk J, Meijer M, Khouri T, Pezzini S, Grauer S, Schreyeck S, Brüne C 2016 Phys. Rev. B 94 081302 Google Scholar
[155]	Wang L X, Yan Y, Zhang L, Liao Z M, Wu H C, Yu D P 2015 Nanoscale 7 16687 Google Scholar
[156]	Sun H P, Wang C M, Zhang S B, Chen R, Zhao Y, Liu C, Liu Q, Chen C, Lu H Z, Xie X C 2020 Phys. Rev. B 102 241406 Google Scholar
[157]	Klitzing K v, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[158]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[159]	Yasuda K, Wakatsuki R, Morimoto T, Yoshimi R, Tsukazaki A, Takahashi K, Ezawa M, Kawasaki M, Nagaosa N, Tokura Y 2016 Nat. Phys. 12 555 Google Scholar
[160]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[161]	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, et al. 2019 Nature 565 337 Google Scholar
[162]	Kang K, Li T, Sohn E, Shan J, Mak K F 2018 arXiv: 1809.08744 [cond-mat]
[163]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[164]	Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003 Google Scholar
[165]	Beenakker C 2013 Annu. Rev. Condens. Matter Phys. 4 113 Google Scholar
[166]	Stanescu T D, Tewari S 2013 J. Phys. Condes. Matter 25 233201 Google Scholar
[167]	Lutchyn R M, Sau J D, Sarma S D 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[168]	Oreg Y, Refael G, Von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[169]	Prada E, San-Jose P, Aguado R 2012 Phys. Rev. B 86 180503 Google Scholar
[170]	Sarma S D, Sau J D, Stanescu T D 2012 Phys. Rev. B 86 220506 Google Scholar
[171]	Rainis D, Trifunovic L, Klinovaja J, Loss D 2013 Phys. Rev. B 87 024515 Google Scholar
[172]	Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C 2016 Nature 531 206 Google Scholar
[173]	Sherman D, Yodh J, Albrecht S M, Nygård J, Krogstrup P, Marcus C M 2017 Nat. Nanotechnol. 12 212 Google Scholar
[174]	Albrecht S, Hansen E, Higginbotham A P, Kuemmeth F, Jespersen T, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus C 2017 Phys. Rev. Lett. 118 137701 Google Scholar
[175]	Vaitiekėnas S, Whiticar A M, Deng M T, Krizek F, Sestoft J E, Palmstrøm C, Martí-Sànchez S, Arbiol J, Krogstrup P, Casparis L 2018 Phys. Rev. Lett. 121 147701 Google Scholar
[176]	O’Farrell E, Drachmann A, Hell M, Fornieri A, Whiticar A, Hansen E, Gronin S, Gardner G, Thomas C, Manfra M 2018 Phys. Rev. Lett. 121 256803 Google Scholar
[177]	Shen J, Heedt S, Borsoi F, Van Heck B, Gazibegovic S, Veld R L O, Car D, Logan J A, Pendharkar M, Ramakers S J 2018 Nat. Commun. 9 4801
[178]	Sánchez D, Serra L 2006 Phys. Rev. B 74 153313 Google Scholar
[179]	Sánchez D, Serra L, Choi M S 2008 Phys. Rev. B 77 035315 Google Scholar
[180]	Glazov M, Sherman E Y 2011 Phys. Rev. Lett. 107 156602 Google Scholar
[181]	Bommer J D, Zhang H, Gül Ö, Nijholt B, Wimmer M, Rybakov F N, Garaud J, Rodic D, Babaev E, Troyer M 2019 Phys. Rev. Lett. 122 187702 Google Scholar
[182]	Vaitiekėnas S, Deng M T, Nygård J, Krogstrup P, Marcus C 2018 Phys. Rev. Lett. 121 037703 Google Scholar
[183]	de Moor M W, Bommer J D, Xu D, Winkler G W, Antipov A E, Bargerbos A, Wang G, Van Loo N, het Veld R L O, Gazibegovic S 2018 New J. Phys. 20 103049 Google Scholar
[184]	Stanescu T D, Lutchyn R M, Sarma S D 2011 Phys. Rev. B 84 144522 Google Scholar
[185]	Reeg C, Loss D, Klinovaja J 2018 Phys. Rev. B 97 165425 Google Scholar
[186]	Van Heck B, Lutchyn R, Glazman L 2016 Phys. Rev. B 93 235431 Google Scholar
[187]	Fu L 2010 Phys. Rev. Lett. 104 056402 Google Scholar
[188]	Hützen R, Zazunov A, Braunecker B, Yeyati A L, Egger R 2012 Phys. Rev. Lett. 109 166403 Google Scholar
[189]	Higginbotham A P, Albrecht S M, Kiršanskas G, Chang W, Kuemmeth F, Krogstrup P, Jespersen T S, Nygård J, Flensberg K, Marcus C M 2015 Nat. Phys. 11 1017 Google Scholar
[190]	Lü H F, Lu H Z, Shen S Q 2016 Phys. Rev. B 93 245418 Google Scholar
[191]	Lee P A, Ramakrishnan T 1985 Rev. Mod. Phys. 57 287 Google Scholar
[192]	Fu B, Wang H W, Shen S Q 2019 Phys. Rev. Lett. 122 246601 Google Scholar
[193]	Wang H W, Fu B, Shen S Q 2020 Phys. Rev. Lett. 124 206603 Google Scholar
[194]	Dyson F J 1962 J. Math. Phys. 3 140 Google Scholar
[195]	Hikami S, Larkin A I, Nagaoka Y 1980 Prog. Theor. Phys. 63 707 Google Scholar
[196]	McCann E, Kechedzhi K, Fal’ko V I, Suzuura H, Ando T, Altshuler B 2006 Phys. Rev. Lett. 97 146805 Google Scholar
[197]	Altshuler B L, Aronov A G, Lee P 1980 Phys. Rev. Lett. 44 1288 Google Scholar
[198]	Fukuyama H 1980 J. Phys. Soc. Jpn. 48 2169 Google Scholar
[199]	Shan W Y, Lu H Z, Shen S Q 2012 Phys. Rev. B 86 125303 Google Scholar
[200]	Berry M V 1984 Proc. R. Soc. A-Math. Phys. 392 45
[201]	Shon N H, Ando T 1998 J. Phys. Soc. Jpn. 67 2421 Google Scholar
[202]	Suzuura H, Ando T 2002 Phys. Rev. Lett. 89 266603 Google Scholar
[203]	Altland A, Zirnbauer M R 1997 Phys. Rev. B 55 1142 Google Scholar
[204]	Akkermans E, Montambaux G 2007 Mesoscopic Physics of Electrons and Photons (Cambridge: Cambridge university press) pp97−100
[205]	Cao H, Tian J, Miotkowski I, Shen T, Hu J, Qiao S, Chen Y P 2012 Phys. Rev. Lett. 108 216803 Google Scholar
[206]	Checkelsky J G, Hor Y S, Liu M H, Qu D X, Cava R J, Ong N 2009 Phys. Rev. Lett. 103 246601 Google Scholar
[207]	Peng H, Lai K, Kong D, Meister S, Chen Y, Qi X L, Zhang S C, Shen Z X, Cui Y 2010 Nat. Mater. 9 225 Google Scholar
[208]	Chen J, Qin H, Yang F, Liu J, Guan T, Qu F, Zhang G, Shi J, Xie X, Yang C, et al. 2010 Phys. Rev. Lett. 105 176602 Google Scholar
[209]	Checkelsky J G, Hor Y S, Cava R J, Ong N 2011 Phys. Rev. Lett. 106 196801 Google Scholar
[210]	Adler S L 1969 Phys. Rev. 177 2426 Google Scholar
[211]	Bell J S, Jackiw R 1969 Il Nuovo Cimento A (1965-1970) 60 47 Google Scholar
[212]	Burkov A 2017 Phys. Rev. B 96 041110 Google Scholar
[213]	Nandy S, Sharma G, Taraphder A, Tewari S 2017 Phys. Rev. Lett. 119 176804 Google Scholar
[214]	Kumar N, Guin S N, Felser C, Shekhar C 2018 Phys. Rev. B 98 041103 Google Scholar
[215]	Wu M, Zheng G, Chu W, Liu Y, Gao W, Zhang H, Lu J, Han Y, Zhou J, Ning W 2018 Phys. Rev. B 98 161110 Google Scholar
[216]	Li H, Wang H W, He H, Wang J, Shen S Q 2018 Phys. Rev. B 97 201110 Google Scholar
[217]	Ma D, Jiang H, Liu H, Xie X 2019 Phys. Rev. B 99 115121 Google Scholar
[218]	Chang M C, Niu Q 1995 Phys. Rev. Lett. 75 1348 Google Scholar
[219]	Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915 Google Scholar
[220]	Jian H Z, Hua J, Qian N, Jun R S 2013 Chin. Phys. Lett. 30 027101 Google Scholar
[221]	Goswami P, Tewari S 2013 Phys. Rev. B 88 245107 Google Scholar
[222]	Zyuzin A, Burkov A 2012 Phys. Rev. B 86 115133 Google Scholar
[223]	Yip S K 2015 arXiv: 1508.01010 [cond-mat]
[224]	Zhang C, Zhang E, Wang W, Liu Y, Chen Z G, Lu S, Liang S, Cao J, Yuan X, Tang L 2017 Nat. Commun. 8 13741
[225]	Breunig O, Wang Z, Taskin A, Lux J, Rosch A, Ando Y 2017 Nat. Commun. 8 15545
[226]	Assaf B, Phuphachong T, Kampert E, Volobuev V, Mandal P, Sánchez-Barriga J, Rader O, Bauer G, Springholz G, De Vaulchier L 2017 Phys. Rev. Lett. 119 106602 Google Scholar
[227]	Zhang M, Wang H, Mu K, Wang P, Niu W, Zhang S, Xiao G, Chen Y, Tong T, Fu D 2018 ACS Nano 12 1537 Google Scholar
[228]	Fleckenstein C, Ziani N T, Trauzettel B 2016 Phys. Rev. B 94 241406 Google Scholar
[229]	Culcer D 2012 Physica E 44 860 Google Scholar
[230]	Mahan G D 2013 Many-particle Physics (New York: Springer Science & Business Media) pp160−174
[231]	Wolos A, Szyszko S, Drabinska A, Kaminska M, Strzelecka S, Hruban A, Materna A, Piersa M, Borysiuk J, Sobczak K 2016 Phys. Rev. B 93 155114 Google Scholar
[232]	Wang J, DaSilva A M, Chang C Z, He K, Jain J K, Samarth N, Ma X C, Xue Q K, Chan M H 2011 Phys. Rev. B 83 245438 Google Scholar
[233]	He H T, Wang G, Zhang T, Sou I K, Wong G K, Wang J N, Lu H Z, Shen S Q, Zhang F C 2011 Phys. Rev. Lett. 106 166805 Google Scholar
[234]	Morimoto T, Zhong S, Orenstein J, Moore J E 2016 Phys. Rev. B 94 245121 Google Scholar
[235]	Gao Y, Yang S A, Niu Q 2017 Phys. Rev. B 95 165135 Google Scholar
[236]	Gao Y, Yang S A, Niu Q 2014 Phys. Rev. Lett. 112 166601 Google Scholar
[237]	Gao Y, Yang S A, Niu Q 2015 Phys. Rev. B 91 214405 Google Scholar
[238]	Goswami P, Pixley J, Sarma S D 2015 Phys. Rev. B 92 075205 Google Scholar
[239]	Andreev A, Spivak B 2018 Phys. Rev. Lett. 120 026601 Google Scholar
[240]	Fu B, Wang H W, Shen S Q 2020 Phys. Rev. B 101 125203 Google Scholar
[241]	Shoenberg D 1984 Magnetic Oscillations in Metals (Cambridge: Cambridge University Press) pp36−67
[242]	Mikitik G, Sharlai Y V 1999 Phys. Rev. Lett. 82 2147 Google Scholar
[243]	Shoenberg D, Stiles P 1964 Proc. R. Soc. A-Math. Phys. 281 62
[244]	Luk’yanchuk I A, Kopelevich Y 2004 Phys. Rev. Lett. 93 166402 Google Scholar
[245]	Novak M, Sasaki S, Segawa K, Ando Y 2015 Phys. Rev. B 91 041203 Google Scholar
[246]	Du J, Wang H, Chen Q, Mao Q, Khan R, Xu B, Zhou Y, Zhang Y, Yang J, Chen B 2016 Sci. China-Phys. Mech. Astron. 59 657406 Google Scholar
[247]	Zhang C L, Yuan Z, Jiang Q D, Tong B, Zhang C, Xie X, Jia S 2017 Phys. Rev. B 95 085202 Google Scholar
[248]	Park J, Lee G, Wolff-Fabris F, Koh Y, Eom M, Kim Y K, Farhan M, Jo Y, Kim C, Shim J 2011 Phys. Rev. Lett. 107 126402 Google Scholar
[249]	Xiang F X, Wang X L, Veldhorst M, Dou S X, Fuhrer M S 2015 Phys. Rev. B 92 035123 Google Scholar
[250]	Tafti F, Gibson Q, Kushwaha S, Haldolaarachchige N, Cava R 2016 Nat. Phys. 12 272 Google Scholar
[251]	Luo Y, Ghimire N J, Wartenbe M, Choi H, Neupane M, McDonald R, Bauer E, Zhu J, Thompson J, Ronning F 2015 Phys. Rev. B 92 205134 Google Scholar
[252]	Arnold F, Naumann M, Wu S C, Sun Y, Schmidt M, Borrmann H, Felser C, Yan B, Hassinger E 2016 Phys. Rev. Lett. 117 146401 Google Scholar
[253]	Klotz J, Wu S C, Shekhar C, Sun Y, Schmidt M, Nicklas M, Baenitz M, Uhlarz M, Wosnitza J, Felser C 2016 Phys. Rev. B 93 121105 Google Scholar
[254]	dos Reis R, Wu S, Sun Y, Ajeesh M, Shekhar C, Schmidt M, Felser C, Yan B, Nicklas M 2016 Phys. Rev. B 93 205102 Google Scholar
[255]	Sergelius P, Gooth J, Bäßler S, Zierold R, Wiegand C, Niemann A, Reith H, Shekhar C, Felser C, Yan B 2016 Sci. Rep. 6 33859
[256]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[257]	Murakawa H, Bahramy M, Tokunaga M, Kohama Y, Bell C, Kaneko Y, Nagaosa N, Hwang H, Tokura Y 2013 Science 342 1490 Google Scholar
[258]	Kumar N, Manna K, Qi Y, Wu S C, Wang L, Yan B, Felser C, Shekhar C 2017 Phys. Rev. B 95 121109 Google Scholar
[259]	Singha R, Pariari A K, Satpati B, Mandal P 2017 Proc. Natl. Acad. Sci. 114 2468 Google Scholar
[260]	Ali M N, Schoop L M, Garg C, Lippmann J M, Lara E, Lotsch B, Parkin S S 2016 Sci. Adv. 2 e1601742 Google Scholar
[261]	Wang X, Pan X, Gao M, Yu J, Jiang J, Zhang J, Zuo H, Zhang M, Wei Z, Niu W 2016 Adv. Electron. Mater. 2
[262]	Lv Y Y, Zhang B B, Li X, Yao S H, Chen Y, Zhou J, Zhang S T, Lu M H, Chen Y F 2016 Appl. Phys. Lett. 108 244101 Google Scholar
[263]	Hu J, Tang Z, Liu J, Zhu Y, Wei J, Mao Z 2017 Phys. Rev. B 96 045127 Google Scholar
[264]	Pan H, Tong B, Yu J, Wang J, Fu D, Zhang S, Wu B, Wan X, Zhang C, Wang X 2018 Sci. Rep. 8 1 Google Scholar
[265]	Hu J, Tang Z, Liu J, Liu X, Zhu Y, Graf D, Myhro K, Tran S, Lau C N, Wei J 2016 Phys. Rev. Lett. 117 016602 Google Scholar
[266]	Hu J, Zhu Y, Graf D, Tang Z, Liu J, Mao Z 2017 Phys. Rev. B 95 205134 Google Scholar
[267]	Qu D X, Hor Y S, Xiong J, Cava R J, Ong N P 2010 Science 329 821 Google Scholar
[268]	Charbonneau M, Van Vliet K, Vasilopoulos P 1982 J. Math. Phys. 23 318 Google Scholar
[269]	Vasilopoulos P, Van Vliet C M 1984 J. Math. Phys. 25 1391 Google Scholar
[270]	Wang C, Lei X 2012 Phys. Rev. B 86 035442 Google Scholar
[271]	Wang C, Lei X 2015 Phys. Rev. B 92 125303 Google Scholar
[272]	Datta S 1997 Electronic Transport in Mesoscopic Dystems (Cambridge: Cambridge university press) pp23−24
[273]	Vasko F T, Raichev O E 2006 Quantum Kinetic Theory and Applications: Electrons, Photons, Phonons (New York: Springer Science & Business Media) pp99−147
[274]	Abrikosov A 1998 Phys. Rev. B 58 2788
[275]	Liu Z, Yang L, Sun Y, Zhang T, Peng H, Yang H, Chen C, Zhang Y, Guo Y, Prabhakaran D 2016 Nat. Mater. 15 27 Google Scholar
[276]	Xiong J, Kushwaha S, Krizan J, Liang T, Cava R J, Ong N P 2016 EPL 114 27002 Google Scholar
[277]	Hu J, Liu J, Graf D, Radmanesh S, Adams D, Chuang A, Wang Y, Chiorescu I, Wei J, Spinu L 2016 Sci. Rep. 6 18674 Google Scholar
[278]	Phillips M, Aji V 2014 Phys. Rev. B 90 115111 Google Scholar
[279]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[280]	Novoselov K, Geim A, Morozov S, Jiang D, Katsnelson M, Grigorieva I, Dubonos S, Firsov A 2005 Nature 438 197 Google Scholar
[281]	Xu Y, Miotkowski I, Liu C, Tian J, Nam H, Alidoust N, Hu J, Shih C K, Hasan M Z, Chen Y P 2014 Nat. Phys. 10 956 Google Scholar
[282]	Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 6627
[283]	Lu H Z 2019 Natl. Sci. Rev. 6 208 Google Scholar
[284]	Hosur P 2012 Phys. Rev. B 86 195102 Google Scholar
[285]	Baum Y, Berg E, Parameswaran S, Stern A 2015 Phys. Rev. X 5 041046
[286]	Gorbar E, Miransky V, Shovkovy I, Sukhachov P 2016 Phys. Rev. B 93 235127 Google Scholar
[287]	Ominato Y, Koshino M 2016 Phys. Rev. B 93 245304 Google Scholar
[288]	McCormick T M, Watzman S J, Heremans J P, Trivedi N 2018 Phys. Rev. B 97 195152 Google Scholar
[289]	Moll P J, Nair N L, Helm T, Potter A C, Kimchi I, Vishwanath A, Analytis J G 2016 Nature 535 266 Google Scholar
[290]	Ruan J, Jian S K, Yao H, Zhang H, Zhang S C, Xing D 2016 Nat. Commun. 7 11136
[291]	Potter A C, Kimchi I, Vishwanath A 2014 Nat. Commun. 5 5161
[292]	Xu S Y, Belopolski I, Sanchez D S, Neupane M, Chang G, Yaji K, Yuan Z, Zhang C, Kuroda K, Bian G 2016 Phys. Rev. Lett. 116 096801 Google Scholar
[293]	Belopolski I, Xu S Y, Sanchez D S, Chang G, Guo C, Neupane M, Zheng H, Lee C C, Huang S M, Bian G 2016 Phys. Rev. Lett. 116 066802 Google Scholar
[294]	Belopolski I, Xu S Y, Ishida Y, Pan X, Yu P, Sanchez D S, Zheng H, Neupane M, Alidoust N, Chang G 2016 Phys. Rev. B 94 085127 Google Scholar
[295]	Xu S Y, Belopolski I, Sanchez D S, Zhang C, Chang G, Guo C, Bian G, Yuan Z, Lu H, Chang T R 2015 Sci. Adv. 1 e1501092 Google Scholar
[296]	Uchida M, Nakazawa Y, Nishihaya S, Akiba K, Kriener M, Kozuka Y, Miyake A, Taguchi Y, Tokunaga M, Nagaosa N 2017 Nat. Commun. 8 2274
[297]	Schumann T, Galletti L, Kealhofer D A, Kim H, Goyal M, Stemmer S 2018 Phys. Rev. Lett. 120 016801 Google Scholar
[298]	Zhang C, Zhang Y, Yuan X, Lu S, Zhang J, Narayan A, Liu Y, Zhang H, Ni Z, Liu R 2019 Nature 565 331 Google Scholar
[299]	Gusynin V, Sharapov S 2005 Phys. Rev. Lett. 95 146801 Google Scholar
[300]	Zyuzin A, Burkov A 2011 Phys. Rev. B 83 195413 Google Scholar
[301]	Zhang S B, Zhang Y Y, Shen S Q 2014 Phys. Rev. B 90 115305 Google Scholar
[302]	Zhang S B, Lu H Z, Shen S Q 2015 Sci. Rep. 5 13277 Google Scholar
[303]	Pertsova A, Canali C M, MacDonald A 2016 Phys. Rev. B 94 121409 Google Scholar
[304]	Zheng H, Xu S Y, Bian G, Guo C, Chang G, Sanchez D S, Belopolski I, Lee C C, Huang S M, Zhang X 2016 ACS Nano 10 1378 Google Scholar
[305]	Ma E Y, Calvo M R, Wang J, Lian B, Mühlbauer M, Brüne C, Cui Y T, Lai K, Kundhikanjana W, Yang Y 2015 Nat. Commun. 6 7252
[306]	Li H, Liu H, Jiang H, Xie X 2020 Phys. Rev. Lett. 125 036602 Google Scholar
[307]	Zhang C, Narayan A, Lu S, Zhang J, Zhang H, Ni Z, Yuan X, Liu Y, Park J H, Zhang E 2017 Nat. Commun. 8 1272
[308]	Lin B C, Wang S, Wiedmann S, Lu J M, Zheng W Z, Yu D, Liao Z M 2019 Phys. Rev. Lett. 122 036602 Google Scholar
[309]	Halperin B I 1987 Jpn. J. Appl. Phys. 26 1913 Google Scholar
[310]	Tang F, Ren Y, Wang P, Zhong R, Schneeloch J, Yang S A, Yang K, Lee P A, Gu G, Qiao Z 2019 Nature 569 537 Google Scholar
[311]	Song Z, Fang Z, Dai X 2017 Phys. Rev. B 96 235104 Google Scholar
[312]	Pan Z, Shindou R 2019 Phys. Rev. B 100 165124 Google Scholar
[313]	Roy B, Sau J D, Sarma S D 2014 Phys. Rev. B 89 165119 Google Scholar
[314]	Grüner G 1988 Rev. Mod. Phys. 60 1129 Google Scholar
[315]	Aji V 2012 Phys. Rev. B 85 241101 Google Scholar
[316]	Ominato Y, Koshino M 2014 Phys. Rev. B 89 054202 Google Scholar
[317]	Song J C, Refael G, Lee P A 2015 Phys. Rev. B 92 180204 Google Scholar
[318]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[319]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[320]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[321]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L 2013 Science 340 167 Google Scholar
[322]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[323]	Akhmerov A, Nilsson J, Beenakker C 2009 Phys. Rev. Lett. 102 216404 Google Scholar
[324]	Belopolski I, Xu S Y, Koirala N, Liu C, Bian G, Strocov V N, Chang G, Neupane M, Alidoust N, Sanchez D 2017 Sci. Adv. 3 e1501692 Google Scholar
[325]	Chiu C K, Bian G, Zheng H, Yin J X, Zhang S S, Sanchez D, Belopolski I, Xu S Y, Hasan M Z 2018 EPL 123 47005 Google Scholar
[326]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[327]	Büttner B, Liu C, Tkachov G, Novik E, Brüne C, Buhmann H, Hankiewicz E, Recher P, Trauzettel B, Zhang S 2011 Nat. Phys. 7 418 Google Scholar
[328]	Mani A, Benjamin C 2017 Sci. Rep. 7 6954
[329]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002
[330]	Liu Y, Yuan X, Zhang C, Jin Z, Narayan A, Luo C, Chen Z, Yang L, Zou J, Wu X 2016 Nat. Commun. 7 12516
[331]	Zhang W, Yu R, Feng W, Yao Y, Weng H, Dai X, Fang Z 2011 Phys. Rev. Lett. 106 156808 Google Scholar
[332]	Sebastian S E, Harrison N, Palm E, Murphy T, Mielke C, Liang R, Bonn D, Hardy W, Lonzarich G 2008 Nature 454 200 Google Scholar
[333]	Li L, Checkelsky J G, Hor Y S, Uher C, Hebard A F, Cava R J, Ong N 2008 Science 321 547 Google Scholar
[334]	Zhang Z, Wei W, Yang F, Zhu Z, Guo M, Feng Y, Yu D, Yao M, Harrison N, McDonald R 2015 Phys. Rev. B 92 235402 Google Scholar
[335]	Mikitik G, Sharlai Y V 2004 Phys. Rev. Lett. 93 106403 Google Scholar
[336]	Mikitik G, Sharlai Y V 1996 Low Temp. Phys. 22 585
[337]	Mikitik G, Sharlai Y V 2016 Phys. Rev. B 94 195123 Google Scholar
[338]	Moll P J, Potter A C, Nair N L, Ramshaw B, Modic K A, Riggs S, Zeng B, Ghimire N J, Bauer E D, Kealhofer R 2016 Nat. Commun. 7 12492
[339]	Koshino M, Hizbullah I F 2016 Phys. Rev. B 93 045201 Google Scholar
[340]	Chen Z G, Chen R, Zhong R, Schneeloch J, Zhang C, Huang Y, Qu F, Yu R, Li Q, Gu G 2017 Proc. Natl. Acad. Sci. 114 816 Google Scholar
[341]	Chen R, Zhang S, Schneeloch J, Zhang C, Li Q, Gu G, Wang N 2015 Phys. Rev. B 92 075107 Google Scholar
[342]	Wu R, Ma J Z, Nie S M, Zhao L X, Huang X, Yin J X, Fu B B, Richard P, Chen G F, Fang Z 2016 Phys. Rev. X 6 021017
[343]	Li X B, Huang W K, Lv Y Y, Zhang K W, Yang C L, Zhang B B, Chen Y, Yao S H, Zhou J, Lu M H 2016 Phys. Rev. Lett. 116 176803 Google Scholar
[344]	Xiong H, Sobota J, Yang S L, Soifer H, Gauthier A, Lu M H, Lv Y Y, Yao S H, Lu D, Hashimoto M 2017 Phys. Rev. B 95 195119 Google Scholar
[345]	Manzoni G, Gragnaniello L, Autès G, Kuhn T, Sterzi A, Cilento F, Zacchigna M, Enenkel V, Vobornik I, Barba L 2016 Phys. Rev. Lett. 117 237601 Google Scholar
[346]	Xu B, Zhao L, Marsik P, Sheveleva E, Lyzwa F, Dai Y, Chen G, Qiu X, Bernhard C 2018 Phys. Rev. Lett. 121 187401 Google Scholar
[347]	Zhang J, Guo C, Zhu X, Ma L, Zheng G, Wang Y, Pi L, Chen Y, Yuan H, Tian M 2017 Phys. Rev. Lett. 118 206601 Google Scholar
[348]	Jones T, Fuller W, Wieting T, Levy F 1982 Solid State Commun. 42 793 Google Scholar
[349]	Behnia K, Aubin H 2016 Rep. Prog. Phys. 79 046502 Google Scholar
[350]	Gooth J, Niemann A C, Meng T, Grushin A G, Landsteiner K, Gotsmann B, Menges F, Schmidt M, Shekhar C, Süß V 2017 Nature 547 324 Google Scholar
[351]	Behnia K, Méasson M A, Kopelevich Y 2007 Phys. Rev. Lett. 98 166602 Google Scholar
[352]	Fauqué B, Zhu Z, Murphy T, Behnia K 2011 Phys. Rev. Lett. 106 246405 Google Scholar
[353]	Fauqué B, Butch N P, Syers P, Paglione J, Wiedmann S, Collaudin A, Grena B, Zeitler U, Behnia K 2013 Phys. Rev. B 87 035133 Google Scholar
[354]	Liang T, Gibson Q, Xiong J, Hirschberger M, Koduvayur S P, Cava R J, Ong N P 2013 Nat. Commun. 4 1
[355]	Zhu Z, Lin X, Liu J, Fauqué B, Tao Q, Yang C, Shi Y, Behnia K 2015 Phys. Rev. Lett. 114 176601 Google Scholar
[356]	Jia Z, Li C, Li X, Shi J, Liao Z, Yu D, Wu X 2016 Nat. Commun. 7 13013
[357]	Liang T, Lin J, Gibson Q, Gao T, Hirschberger M, Liu M, Cava R J, Ong N P 2017 Phys. Rev. Lett. 118 136601 Google Scholar
[358]	Matusiak M, Cooper J, Kaczorowski D 2017 Nat. Commun. 8 15219
[359]	Watzman S J, McCormick T M, Shekhar C, Wu S C, Sun Y, Prakash A, Felser C, Trivedi N, Heremans J P 2018 Phys. Rev. B 97 161404 Google Scholar
[360]	Zhang Y, Wang C, Yu L, Liu G, Liang A, Huang J, Nie S, Sun X, Zhang Y, Shen B, et al. 2017 Nat. Commun. 8 15512 Google Scholar
[361]	Stockert U, Dos Reis R, Ajeesh M, Watzman S, Schmidt M, Shekhar C, Heremans J, Felser C, Baenitz M, Nicklas M 2017 J. Phys.-Condes. Matter 29 325701 Google Scholar
[362]	Wang J, Niu J, Yan B, Li X, Bi R, Yao Y, Yu D, Wu X 2018 Proc. Natl. Acad. Sci. 115 9145 Google Scholar
[363]	Skinner B, Fu L 2018 Sci. Adv. 4 eaat2621 Google Scholar
[364]	Raikh M, Shahbazyan T 1993 Phys. Rev. B 47 1522 Google Scholar
[365]	Pesin D, Mishchenko E, Levchenko A 2015 Phys. Rev. B 92 174202 Google Scholar
[366]	Wang H W, Fu B, Shen S Q 2018 Phys. Rev. B 98 081202 Google Scholar
[367]	Alexandradinata A, Glazman L 2017 Phys. Rev. Lett. 119 256601 Google Scholar
[368]	Alexandradinata A, Wang C, Duan W, Glazman L 2018 Phys. Rev. X 8 011027
[369]	Hoeller J, Alexandradinata A 2018 Phys. Rev. B 98 024310 Google Scholar
[370]	O’Brien T, Diez M, Beenakker C 2016 Phys. Rev. Lett. 116 236401 Google Scholar
[371]	Fei F, Bo X, Wang R, Wu B, Jiang J, Fu D, Gao M, Zheng H, Chen Y, Wang X 2017 Phys. Rev. B 96 041201 Google Scholar
[372]	Yang H, Moessner R, Lim L K 2018 Phys. Rev. B 97 165118 Google Scholar
[373]	Oroszlány L, Dóra B, Cserti J, Cortijo A 2018 Phys. Rev. B 97 205107 Google Scholar
[374]	Zhang Y, Bulmash D, Hosur P, Potter A C, Vishwanath A 2016 Sci. Rep. 6 23741 Google Scholar
[375]	Wang H, Liu H, Li Y, Liu Y, Wang J, Liu J, Dai J Y, Wang Y, Li L, Yan J 2018 Sci. Adv. 4 eaau5096 Google Scholar
[376]	Wang H, Liu Y, Liu Y, Xi C, Wang J, Liu J, Wang Y, Li L, Lau S P, Tian M 2019 Natl. Sci. Rev. 6 914 Google Scholar
[377]	Zhang P, Zhai H 2018 Front. Phys. 13 137204 Google Scholar
[378]	Liu H, Jiang H, Wang Z, Joynt R, Xie X 2018 arXiv: 1807.02459 [cond-mat]
[379]	Weng H, Fang C, Fang Z, Dai X 2016 Phys. Rev. B 93 241202 Google Scholar
[380]	Weng H, Fang C, Fang Z, Dai X 2016 Phys. Rev. B 94 165201 Google Scholar
[381]	Bradlyn B, Cano J, Wang Z, Vergniory M, Felser C, Cava R, Bernevig B A 2016 Science 353Google Scholar
[382]	Chang G, Xu S Y, Huang S M, Sanchez D S, Hsu C H, Bian G, Yu Z M, Belopolski I, Alidoust N, Zheng H 2017 Sci. Rep. 7 1688
[383]	Lv B, Feng Z L, Xu Q N, Gao X, Ma J Z, Kong L Y, Richard P, Huang Y B, Strocov V, Fang C 2017 Nature 546 627 Google Scholar
[384]	Ma J Z, He J B, Xu Y F, Lv B, Chen D, Zhu W L, Zhang S, Kong L Y, Gao X, Rong L Y 2018 Nat. Phys. 14 349 Google Scholar
[385]	He J, Chen D, Zhu W, Zhang S, Zhao L, Ren Z, Chen G 2017 Phys. Rev. B 95 195165 Google Scholar
[386]	Zhu W, He J, Zhang S, Chen D, Shan L, Ren Z, Chen G 2017 arXiv: 1707.00942 [cond-mat]
[387]	Kumar N, Sun Y, Nicklas M, Watzman S J, Young O, Leermakers I, Hornung J, Klotz J, Gooth J, Manna K 2019 Nat. Commun. 10 2475
[388]	Felser C, Yan B 2016 Nat. Mater. 15 1149 Google Scholar
[389]	Nayak A K, Fischer J E, Sun Y, Yan B, Karel J, Komarek A C, Shekhar C, Kumar N, Schnelle W, Kübler J 2016 Sci. Adv. 2 e1501870 Google Scholar
[390]	Wang Z, Vergniory M, Kushwaha S, Hirschberger M, Chulkov E, Ernst A, Ong N P, Cava R J, Bernevig B A 2016 Phys. Rev. Lett. 117 236401 Google Scholar
[391]	Chang G, Xu S Y, Zheng H, Singh B, Hsu C H, Bian G, Alidoust N, Belopolski I, Sanchez D S, Zhang S 2016 Sci. Rep. 6 38839
[392]	Nie S, Xu G, Prinz F B, Zhang S C 2017 Proc. Natl. Acad. Sci. 114 10596 Google Scholar
[393]	Yang H, Sun Y, Zhang Y, Shi W J, Parkin S S, Yan B 2017 New J. Phys. 19 015008 Google Scholar
[394]	Liu E, Sun Y, Kumar N, Muechler L, Sun A, Jiao L, Yang S Y, Liu D, Liang A, Xu Q 2018 Nat. Phys. 14 1125 Google Scholar
[395]	Wang Q, Xu Y, Lou R, Liu Z, Li M, Huang Y, Shen D, Weng H, Wang S, Lei H 2018 Nat. Commun. 9 3681
[396]	Guin S N, Manna K, Noky J, Watzman S J, Fu C, Kumar N, Schnelle W, Shekhar C, Sun Y, Gooth J 2019 NPG Asia Mater. 11 1 Google Scholar
[397]	Chang G, Singh B, Xu S Y, Bian G, Huang S M, Hsu C H, Belopolski I, Alidoust N, Sanchez D S, Zheng H 2018 Phys. Rev. B 97 041104 Google Scholar
[398]	Yin J X, Zhang S S, Li H, Jiang K, Chang G, Zhang B, Lian B, Xiang C, Belopolski I, Zheng H 2018 Nature 562 91 Google Scholar
[399]	Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A 2015 Nature 527 495 Google Scholar
[400]	Deng K, Wan G, Deng P, Zhang K, Ding S, Wang E, Yan M, Huang H, Zhang H, Xu Z 2016 Nat. Phys. 12 1105 Google Scholar
[401]	Jiang J, Liu Z, Sun Y, Yang H, Rajamathi C, Qi Y, Yang L, Chen C, Peng H, Hwang C 2017 Nat. Commun. 8 13973
[402]	Wang Y, Liu E, Liu H, Pan Y, Zhang L, Zeng J, Fu Y, Wang M, Xu K, Huang Z 2016 Nat. Commun. 7 13142
[403]	Zhang E, Chen R, Huang C, Yu J, Zhang K, Wang W, Liu S, Ling J, Wan X, Lu H Z 2017 Nano Lett. 17 878 Google Scholar
[404]	Chen D, Zhao L, He J, Liang H, Zhang S, Li C, Shan L, Wang S, Ren Z, Ren C 2016 Phys. Rev. B 94 174411 Google Scholar
[405]	Khim S, Koepernik K, Efremov D V, Klotz J, Förster T, Wosnitza J, Sturza M I, Wurmehl S, Hess C, van den Brink J 2016 Phys. Rev. B 94 165145 Google Scholar
[406]	Xu S Y, Alidoust N, Chang G, Lu H, Singh B, Belopolski I, Sanchez D S, Zhang X, Bian G, Zheng H 2017 Sci. Adv. 3 e1603266 Google Scholar
[407]	Belopolski I, Sanchez D S, Ishida Y, Pan X, Yu P, Xu S Y, Chang G, Chang T R, Zheng H, Alidoust N 2016 Nat. Commun. 7 13643
[408]	Chang G, Xu S Y, Sanchez D S, Huang S M, Lee C C, Chang T R, Bian G, Zheng H, Belopolski I, Alidoust N 2016 Sci. Adv. 2 e1600295 Google Scholar
[409]	Zhong C, Chen Y, Yu Z M, Xie Y, Wang H, Yang S A, Zhang S 2017 Nat. Commun. 8 15641 Google Scholar
[410]	Chen W, Lu H Z, Hou J M 2017 Phys. Rev. B 96 041102 Google Scholar
[411]	Yan Z, Bi R, Shen H, Lu L, Zhang S C, Wang Z 2017 Phys. Rev. B 96 041103 Google Scholar
[412]	Ezawa M 2017 Phys. Rev. B 96 041202 Google Scholar
[413]	Wang C, Lu H Z, Xie X 2020 Phys. Rev. B 102 041204 Google Scholar
[414]	Hu Y, Liu H, Jiang H, Xie X 2017 Phys. Rev. B 96 134201 Google Scholar
[415]	Wang L X, Li C Z, Yu D P, Liao Z M 2016 Nat. Commun. 7 10769 Google Scholar
[416]	Zheng H, Bian G, Chang G, Lu H, Xu S Y, Wang G, Chang T R, Zhang S, Belopolski I, Alidoust N 2016 Phys. Rev. Lett. 117 266804 Google Scholar
[417]	Zheng H, Zahid Hasan M 2018 Adv. Phys. X 3 1466661
[418]	Zheng H, Chang G, Huang S M, Guo C, Zhang X, Zhang S, Yin J, Xu S Y, Belopolski I, Alidoust N 2017 Phys. Rev. Lett. 119 196403 Google Scholar
[419]	Chang G, Xu S Y, Zheng H, Lee C C, Huang S M, Belopolski I, Sanchez D S, Bian G, Alidoust N, Chang T R 2016 Phys. Rev. Lett. 116 066601 Google Scholar
[420]	Wang S, Lin B C, Zheng W Z, Yu D, Liao Z M 2018 Phys. Rev. Lett. 120 257701 Google Scholar

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