本征磁性拓扑绝缘体MnBi<sub>2</sub>Te<sub>4</sub>研究进展

谢向男; 李成; 曾俊炜; 周珅; 江天

doi:10.7498/aps.72.20230704

摘要

本征磁性拓扑绝缘体非平庸拓扑态和磁有序的相互作用使其具备量子反常霍尔效应和轴子绝缘体等奇异物理性质, 在低功耗拓扑自旋电子器件及拓扑量子计算等方面展现广泛应用前景. 自2019年第一种本征磁性拓扑绝缘体MnBi₂Te₄在实验上被发现以来, 该材料体系领域迅速吸引了大量研究者的目光, 引发了研究热潮. 本文将从MnBi₂Te₄基本性质出发, 介绍近期本征磁性拓扑绝缘体MnBi₂Te₄的一些重要研究成果, 着重阐述MnBi₂Te₄系列的量子反常霍尔效应、轴子绝缘体态和马约拉纳零能模等拓扑量子态, 并列举该材料体系其他研究方向及目前存在的问题. 最后, 总结并展望MnBi₂Te₄的下一步研究, 期望为相关领域人员的研究提供一定参考价值.

关键词:

Abstract

The interaction between non-trivial topological states and the magnetic order of intrinsic magnetic topological insulators gives rise to various exotic physical properties, including the quantum anomalous Hall effect and axion insulator. These materials possess great potential applications in low-power topological spintronic devices and topological quantum computation. Since the first intrinsic magnetic topological insulator, MnBi₂Te₄, was discovered in 2019, this material system has received significant attention from researchers and sparked a research boom. This paper begins with discussing the fundamental properties of MnBi₂Te₄ and then turns to important research findings related to this intrinsic magnetic topological insulator. Specifically, it focuses on the quantum anomalous Hall effect, axion insulating state, and Majorana zero energy mode exhibited by the MnBi₂Te₄ series. Furthermore, this paper highlights other research directions and current challenges associated with this material system. Finally, this paper provides a summary and outlook for future research on MnBi₂Te₄, aiming to offer valuable references for researchers in related fields.

Keywords:

intrinsic magnetic topological insulators /
MnBi₂Te₄ /
topological quantum states

作者及机构信息

1.
国防科技大学理学院, 量子信息研究所, 长沙　410073

2.
国防科技大学计算机学院, 量子信息研究所兼高性能计算国家重点实验室, 长沙　410073

通信作者: 江天, tjiang@nudt.edu.cn

基金项目: 高性能计算国家重点实验室自主开放课题(批准号: 202201-04)资助的课题.

Authors and contacts

1.
Institute for Quantum Information, College of Science, National University of Defense Technology, Changsha 410073, China

2.
State Key Laboratory of High Performance Computing, Institute for Quantum Information, College of Computer, National University of Defense Technology, Changsha 410073, China

Corresponding author: Jiang Tian, tjiang@nudt.edu.cn

Funds: Project supported by the Independent and Open Subject Fund from State Key Laboratory of High Performance Computing, China (Grant No. 202201-04).

文章全文

参考文献

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[2]	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
[3]	Fu L, Kane C L 2007 Phys. Rev. B 76 045302 Google Scholar
[4]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[5]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[6]	Pesin D, MacDonald A H 2012 Nat. Mater. 11 409 Google Scholar
[7]	Rajamathi C R, Gupta U, Kumar N, Yang H, Sun Y, Suss V, Shekhar C, Schmidt M, Blumtritt H, Werner P, Yan B H, Parkin S, Felser C, Rao C N R 2017 Adv. Mater. 29 1606202 Google Scholar
[8]	Kitaev A Y 2003 Ann. Phys. 303 2 Google Scholar
[9]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[10]	Chang C Z, Zhao W, Kim D Y, Zhang H, Assaf B A, Heiman D, Zhang S C, Liu C, Chan M H W, Moodera J S 2015 Nat. Mater. 14 473 Google Scholar
[11]	Mogi M, Kawamura M, Yoshimi R, Tsukazaki A, Kozuka Y, Shirakawa N, Takahashi K S, Kawasaki M, Tokura Y 2017 Nat. Mater. 16 516 Google Scholar
[12]	Xiao D, Jiang J, Shin J H, Wang W, Wang F, Zhao Y F, Liu C, Wu W, Chan M H W, Samarth N, Chang C Z 2018 Phys. Rev. Lett. 120 056801 Google Scholar
[13]	Lachman E O, Young A F, Richardella A, Cuppens J, Naren H R, Anahory Y, Meltzer A Y, Kandala A, Kempinger S, Myasoedov Y, Huber M E, Samarth N, Zeldov E 2015 Sci. Adv. 1 e1500740 Google Scholar
[14]	Otrokov M M, Menshchikova T V, Vergniory M G, Rusinov I P, Yu Vyazovskaya A, Koroteev Y M, Bihlmayer G, Ernst A, Echenique P M, Arnau A, Chulkov E V 2017 2D Mater. 4 025082 Google Scholar
[15]	Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401 Google Scholar
[16]	Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, Xu Y 2019 Sci. Adv. 5 eaaw5685 Google Scholar
[17]	Otrokov M M, Rusinov I P, Blanco-Rey M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, Chulkov E V 2019 Phys. Rev. Lett. 122 107202 Google Scholar
[18]	Qi X L, Hughes T L, Zhang S C 2008 Phys. Rev. B 78 195424 Google Scholar
[19]	Peng Y, Xu Y 2019 Phys. Rev. B 99 195431 Google Scholar
[20]	He Q L, Hughes T L, Armitage N P, Tokura Y, Wang K L 2022 Nat. Mater. 21 15 Google Scholar
[21]	Chen X, Wang H, Liu H, Wang C, Wei G, Fang C, Wang H, Geng C, Liu S, Li P, Yu H, Zhao W, Miao J, Li Y, Wang L, Nie T, Zhao J, Wu X 2022 Adv. Mater. 34 2106172 Google Scholar
[22]	Flensberg K, von Oppen F, Stern A 2021 Nat. Rev. Mater. 6 944 Google Scholar
[23]	Wang Y, Ma X M, Hao Z, Cai Y, Rong H, Zhang F, Chen W, Zhang C, Lin J, Zhao Y, Liu C, Liu Q, Chen C 2023 Natl. Sci. Rev. DOI: 10.1093/nsr/nwad066
[24]	Tokura Y, Yasuda K, Tsukazaki A 2019 Nat. Rev. Phys. 1 126 Google Scholar
[25]	Mogi M, Kawamura M, Tsukazaki A, Yoshimi R, Takahashi K S, Kawasaki M, Tokura Y 2017 Sci. Adv. 3 eaao1669 Google Scholar
[26]	Lian B, Sun X Q, Vaezi A, Qi X L, Zhang S C 2018 Proc. Natl. Acad. Sci. U. S. A. 115 10938 Google Scholar
[27]	Mong R S K, Essin A M, Moore J E 2010 Phys. Rev. B 81 245209 Google Scholar
[28]	Lee D S, Kim T H, Park C H, Chung C Y, Lim Y S, Seo W S, Park H H 2013 CrystEngComm 15 5532 Google Scholar
[29]	Gong Y, Guo J, Li J, Zhu K, Liao M, Liu X, Zhang Q, Gu L, Tang L, Feng X, Zhang D, Li W, Song C, Wang L, Yu P, Chen X, Wang Y, Yao H, Duan W, Xu Y, Zhang S C, Ma X, Xue Q K, He K 2019 Chin. Phys. Lett. 36 076801 Google Scholar
[30]	Otrokov M M, Klimovskikh I I, Bentmann H, Estyunin D, Zeugner A, Aliev Z S, Gass S, Wolter A U B, Koroleva A V, Shikin A M, Blanco-Rey M, Hoffmann M, Rusinov I P, Vyazovskaya A Y, Eremeev S V, Koroteev Y M, Kuznetsov V M, Freyse F, Sánchez-Barriga J, Amiraslanov I R, Babanly M B, Mamedov N T, Abdullayev N A, Zverev V N, Alfonsov A, Kataev V, Buchner B, Schwier E F, Kumar S, Kimura A, Petaccia L, Di Santo G, Vidal R C, Schatz S, Kissner K, Unzelmann M, Min C H, Moser S, Peixoto T R F, Reinert F, Ernst A, Echenique P M, Isaeva A, Chulkov E V 2019 Nature 576 416 Google Scholar
[31]	Deng Y, Yu Y, Shi M Z, Guo Z, Xu Z, Wang J, Chen X H, Zhang Y 2020 Science 367 895 Google Scholar
[32]	Liu C, Wang Y, Li H, Wu Y, Li Y, Li J, He K, Xu Y, Zhang J, Wang Y 2020 Nat. Mater. 19 522 Google Scholar
[33]	Ge J, Liu Y, Li J, Li H, Luo T, Wu Y, Xu Y, Wang J 2020 Natl. Sci. Rev. 7 1280 Google Scholar
[34]	Li Y, Liu C, Wang Y, Lian Z, Li H, Chun O, Zhang J, Wang Y 2021 arXiv: 2105.10390v1 [cond-mat. mtrl-sci
[35]	Liu C, Wang Y, Yang M, Mao J, Li H, Li Y, Li J, Zhu H, Wang J, Li L, Wu Y, Xu Y, Zhang J, Wang Y 2021 Nat. Commun. 12 4647 Google Scholar
[36]	Wu M, Tu D, Nie Y, Miao S, Gao W, Han Y, Zhu X, Zhou J, Ning W, Tian M 2022 Nano Lett. 22 73 Google Scholar
[37]	Gao A, Liu Y F, Hu C, Qiu J X, Tzschaschel C, Ghosh B, Ho S C, Bérubé D, Chen R, Sun H, Zhang Z, Zhang X Y, Wang Y X, Wang N, Huang Z, Felser C, Agarwal A, Ding T, Tien H J, Akey A, Gardener J, Singh B, Watanabe K, Taniguchi T, Burch K S, Bell D C, Zhou B B, Gao W, Lu H Z, Bansil A, Lin H, Chang T R, Fu L, Ma Q, Ni N, Xu S Y 2021 Nature 595 521 Google Scholar
[38]	Tai L, Chong S K, Zhang H, Zhang P, Deng P, Eckberg C, Qiu G, Dai B, He H, wu D, Xu S, Davydov A, Wang K 2021 arXiv: 2103.09878v1 [cond-mat. mtrl-sci
[39]	Ye C, Xie X, Lü W, Huang K, Yang A J, Jiang S, Liu X, Zhu D, Qiu X, Tong M, Zhou T, Hsu C H, Chang G, Lin H, Li P, Yang K, Wang Z, Jiang T, Renshaw Wang X 2022 Nano Lett. 22 1366 Google Scholar
[40]	Zhang Z, Wang N, Cao N, Wang A, Zhou X, Watanabe K, Taniguchi T, Yan B, Gao W B 2022 Nat. Commun. 13 6191 Google Scholar
[41]	Bartram F M, Leng Y C, Wang Y, Liu L, Chen X, Peng H, Li H, Yu P, Wu Y, Lin M L, Zhang J, Tan P H, Yang L 2022 npj Quantum Mater. 7 84 Google Scholar
[42]	占国慧, 王怀强, 张海军 2020 物理 49 817 Google Scholar Zhan G H, Wang H Q, Zhang H J 2020 Physics 49 817 Google Scholar
[43]	郭文锑, 黄璐, 许桂贵, 钟克华, 张健敏, 黄志高 2021 70 047101 Google Scholar Guo W T, Huang L, Xu G G, Zhong K H, Zhang J M, Huang Z G 2021 Acta Phys. Sin. 70 047101 Google Scholar
[44]	Wang Y, Zhang F, Zeng M, Sun H, Hao Z, Cai Y, Rong H, Zhang C, Liu C, Ma X, Wang L, Guo S, Lin J, Liu Q, Liu C, Chen C 2023 Front. Phys. 18 21304 Google Scholar
[45]	Li B, Yan J Q, Pajerowski D M, Gordon E, Nedić A M, Sizyuk Y, Ke L, Orth P P, Vaknin D, McQueeney R J 2020 Phys. Rev. Lett. 124 167204 Google Scholar
[46]	Yan J Q, Zhang Q, Heitmann T, Huang Z, Chen K Y, Cheng J G, Wu W, Vaknin D, Sales B C, McQueeney R J 2019 Phys. Rev. Mater. 3 064202 Google Scholar
[47]	Yang S, Xu X, Zhu Y, Niu R, Xu C, Peng Y, Cheng X, Jia X, Huang Y, Xu X, Lu J, Ye Y 2021 Phys. Rev. X 11 011003 Google Scholar
[48]	Wang P, Ge J, Li J, Liu Y, Xu Y, Wang J 2021 The Innovation 2 100098 Google Scholar
[49]	Li J, Wang C, Zhang Z, Gu B-L, Duan W, Xu Y 2019 Phys. Rev. B 100 121103 Google Scholar
[50]	Deng H, Chen Z, Wołoś A, Konczykowski M, Sobczak K, Sitnicka J, Fedorchenko I V, Borysiuk J, Heider T, Pluciński Ł, Park K, Georgescu A B, Cano J, Krusin-Elbaum L 2021 Nat. Phys. 17 36 Google Scholar
[51]	Fu H, Liu C X, Yan B 2020 Sci. Adv. 6 eaaz0948 Google Scholar
[52]	Gao R, Qin G, Qi S, Qiao Z, Ren W 2021 Phys. Rev. Mater. 5 114201 Google Scholar
[53]	Ying Z, Zhang S, Chen B, Jia B, Fei F, Zhang M, Zhang H, Wang X, Song F 2022 Phys. Rev. B 105 085412 Google Scholar
[54]	Nomura K, Nagaosa N 2011 Phys. Rev. Lett. 106 166802 Google Scholar
[55]	Li H, Jiang H, Chen C Z, Xie X C 2021 Phys. Rev. Lett. 126 156601 Google Scholar
[56]	Tse W K, MacDonald A H 2010 Phys. Rev. Lett. 105 057401 Google Scholar
[57]	Wu L, Salehi M, Koirala N, Moon J, Oh S, Armitage N P 2016 Science 354 1124 Google Scholar
[58]	Wang J, Lian B, Qi X L, Zhang S C 2015 Phys. Rev. B 92 081107 Google Scholar
[59]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
[60]	Wilczek F 1987 Phys. Rev. Lett. 58 1799 Google Scholar
[61]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[62]	Wang J 2020 Sci. Chin. -Phys. , Mech. Astron. 63 127031 Google Scholar
[63]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[64]	Qi X L, Hughes T L, Zhang S C 2010 Phys. Rev. B 82 184516 Google Scholar
[65]	't Hooft G 1976 Phys. Rev. D 14 3421 Google Scholar
[66]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[67]	Chen C, Jiang K, Zhang Y, Liu C, Liu Y, Wang Z, Wang J 2020 Nat. Phys. 16 536 Google Scholar
[68]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[69]	Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003 Google Scholar
[70]	Stone M, Roy R 2004 Phys. Rev. B 69 184511 Google Scholar
[71]	Wang M X, Liu C, Xu J P, Yang F, Miao L, Yao M Y, Gao C L, Shen C, Ma X, Chen X, Xu Z A, Liu Y, Zhang S C, Qian D, Jia J F, Xue Q K 2012 Science 336 52 Google Scholar
[72]	Fu L, Kane C L 2009 Phys. Rev. Lett. 102 216403 Google Scholar
[73]	Sau J D, Lutchyn R M, Tewari S, Das Sarma S 2010 Phys. Rev. Lett. 104 040502 Google Scholar
[74]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[75]	Akhmerov A R, Nilsson J, Beenakker C W J 2009 Phys. Rev. Lett. 102 216404 Google Scholar
[76]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[77]	Fu L, Kane C L 2009 Phys. Rev. B 79 161408 Google Scholar
[78]	Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G D, Ding H, Shin S 2018 Science 360 182 Google Scholar
[79]	Kong L, Zhu S, Papaj M, Chen H, Cao L, Isobe H, Xing Y, Liu W, Wang D, Fan P, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Gao H J, Ding H 2019 Nat. Phys. 15 1181 Google Scholar
[80]	König E J, Coleman P 2019 Phys. Rev. Lett. 122 207001 Google Scholar
[81]	Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T, Tamegai T 2019 Nat. Mater. 18 811 Google Scholar
[82]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[83]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[84]	Xu J P, Wang M X, Liu Z L, Ge J F, Yang X, Liu C, Xu Z A, Guan D, Gao C L, Qian D, Liu Y, Wang Q H, Zhang F C, Xue Q K, Jia J F 2015 Phys. Rev. Lett. 114 017001 Google Scholar
[85]	Sun H H, Zhang K W, Hu L H, Li C, Wang G Y, Ma H Y, Xu Z A, Gao C L, Guan D D, Li Y Y, Liu C, Qian D, Zhou Y, Fu L, Li S C, Zhang F C, Jia J F 2016 Phys. Rev. Lett. 116 257003 Google Scholar
[86]	何映萍, 洪健松, 刘雄军 2020 69 110302 Google Scholar He Y P, Hong J S, Liu X J 2020 Acta Phys. Sin. 69 110302 Google Scholar
[87]	Strübi G, Belzig W, Choi M S, Bruder C 2011 Phys. Rev. Lett. 107 136403 Google Scholar
[88]	Chung S B, Qi X L, Maciejko J, Zhang S C 2011 Phys. Rev. B 83 100512 Google Scholar
[89]	Wang J, Zhou Q, Lian B, Zhang S-C 2015 Phys. Rev. B 92 064520 Google Scholar
[90]	Maciejko J, Qi X L, Drew H D, Zhang S C 2010 Phys. Rev. Lett. 105 166803 Google Scholar
[91]	Wang J, Lian B, Zhang S C 2014 Phys. Rev. B 89 085106 Google Scholar
[92]	Yan Q, Li H, Zeng J, Sun Q F, Xie X C 2021 Commun. Phys. 4 239 Google Scholar
[93]	Zhang X, Liu F 2021 Phys. Rev. B 103 024405 Google Scholar
[94]	Chen L, Cao Z, He K, Liu X, Liu D E 2023 Phys. Rev. B 107 165405 Google Scholar
[95]	Klimovskikh I I, Otrokov M M, Estyunin D, Eremeev S V, Filnov S O, Koroleva A, Shevchenko E, Voroshnin V, Rybkin A G, Rusinov I P, Blanco-Rey M, Hoffmann M, Aliev Z S, Babanly M B, Amiraslanov I R, Abdullayev N A, Zverev V N, Kimura A, Tereshchenko O E, Kokh K A, Petaccia L, Di Santo G, Ernst A, Echenique P M, Mamedov N T, Shikin A M, Chulkov E V 2020 npj Quantum Mater. 5 54 Google Scholar
[96]	Chen P, Yao Q, Xu J, Sun Q, Grutter A J, Quarterman P, Balakrishnan P P, Kinane C J, Caruana A J, Langridge S, Li A, Achinuq B, Heppell E, Ji Y, Liu S, Cui B, Liu J, Huang P, Liu Z, Yu G, Xiu F, Hesjedal T, Zou J, Han X, Zhang H, Yang Y, Kou X 2023 Nat. Electron. 6 18 Google Scholar
[97]	Tian S, Gao S, Nie S, Qian Y, Gong C, Fu Y, Li H, Fan W, Zhang P, Kondo T, Shin S, Adell J, Fedderwitz H, Ding H, Wang Z, Qian T, Lei H 2020 Phys. Rev. B 102 035144 Google Scholar
[98]	Hu C, Ding L, Gordon K N, Ghosh B, Tien H-J, Li H, Linn A G, Lien S W, Huang C Y, Mackey S, Liu J, Reddy P V S, Singh B, Agarwal A, Bansil A, Song M, Li D, Xu S Y, Lin H, Cao H, Chang T R, Dessau D, Ni N 2020 Science advances 6 eaba4275 Google Scholar
[99]	Wu J, Liu F, Liu C, Wang Y, Li C, Lu Y, Matsuishi S, Hosono H 2020 Adv. Mater. 32 2001815 Google Scholar
[100]	Shi M Z, Lei B, Zhu C S, Ma D H, Cui J H, Sun Z L, Ying J J, Chen X H 2019 Phys. Rev. B 100 155144 Google Scholar
[101]	Ding L, Hu C, Ye F, Feng E, Ni N, Cao H 2020 Phys. Rev. B 101 020412 Google Scholar
[102]	Hu Y, Xu L, Shi M, Luo A, Peng S, Wang Z Y, Ying J J, Wu T, Liu Z K, Zhang C F, Chen Y L, Xu G, Chen X H, He J F 2020 Phys. Rev. B 101 161113 Google Scholar
[103]	Jo N H, Wang L L, Slager R J, Yan J, Wu Y, Lee K, Schrunk B, Vishwanath A, Kaminski A 2020 Phys. Rev. B 102 045130 Google Scholar
[104]	Zhang R X, Wu F, Das Sarma S 2020 Phys. Rev. Lett. 124 136407 Google Scholar
[105]	Yan J Q, Liu Y H, Parker D S, Wu Y, Aczel A A, Matsuda M, McGuire M A, Sales B C 2020 Phys. Rev. Mater. 4 054202 Google Scholar
[106]	Hu C, Gordon K N, Liu P, Liu J, Zhou X, Hao P, Narayan D, Emmanouilidou E, Sun H, Liu Y, Brawer H, Ramirez A P, Ding L, Cao H, Liu Q, Dessau D, Ni N 2020 Nat. Commun. 11 97 Google Scholar
[107]	Vidal R C, Zeugner A, Facio J I, Ray R, Haghighi M H, Wolter A U B, Corredor Bohorquez L T, Caglieris F, Moser S, Figgemeier T, Peixoto T R F, Vasili H B, Valvidares M, Jung S, Cacho C, Alfonsov A, Mehlawat K, Kataev V, Hess C, Richter M, Büchner B, van den Brink J, Ruck M, Reinert F, Bentmann H, Isaeva A 2019 Phys. Rev. X 9 041065 Google Scholar
[108]	He K 2020 npj Quantum Mater. 5 90 Google Scholar
[109]	Xie H K, Wang D H, Cai Z X, Chen B, Guo J W, Naveed M, Zhang S, Zhang M H, Wang X F, Fei F C, Zhang H J, Song F Q 2020 Appl. Phys. Lett. 116 221902 Google Scholar
[110]	Xu X, Yang S, Wang H, Guzman R, Gao Y, Zhu Y, Peng Y, Zang Z, Xi M, Tian S, Li Y, Lei H, Luo Z, Yang J, Wang Y, Xia T, Zhou W, Huang Y, Ye Y 2022 Nat. Commun. 13 7646 Google Scholar
[111]	Wu X, Li J, Ma X M, Zhang Y, Liu Y, Zhou C-S, Shao J, Wang Q, Hao Y J, Feng Y, Schwier E F, Kumar S, Sun H, Liu P, Shimada K, Miyamoto K, Okuda T, Wang K, Xie M, Chen C, Liu Q, Liu C, Zhao Y 2020 Phys. Rev. X 10 031013 Google Scholar
[112]	Rienks E D L, Wimmer S, Sánchez-Barriga J, Caha O, Mandal P S, Růžička J, Ney A, Steiner H, Volobuev V V, Groiss H, Albu M, Kothleitner G, Michalička J, Khan S A, Minár J, Ebert H, Bauer G, Freyse F, Varykhalov A, Rader O, Springholz G 2019 Nature 576 423 Google Scholar
[113]	Lu R, Sun H, Kumar S, Wang Y, Gu M, Zeng M, Hao Y J, Li J, Shao J, Ma X M, Hao Z, Zhang K, Mansuer W, Mei J, Zhao Y, Liu C, Deng K, Huang W, Shen B, Shimada K, Schwier E F, Liu C, Liu Q, Chen C 2021 Phys. Rev. X 11 011039 Google Scholar
[114]	Sun H, Xia B, Chen Z, Zhang Y, Liu P, Yao Q, Tang H, Zhao Y, Xu H, Liu Q 2019 Phys. Rev. Lett. 123 096401 Google Scholar
[115]	Gu M, Li J, Sun H, Zhao Y, Liu C, Liu J, Lu H, Liu Q 2021 Nat. Commun. 12 3524 Google Scholar
[116]	Chen B, Fei F, Zhang D, Zhang B, Liu W, Zhang S, Wang P, Wei B, Zhang Y, Zuo Z, Guo J, Liu Q, Wang Z, Wu X, Zong J, Xie X, Chen W, Sun Z, Wang S, Zhang Y, Zhang M, Wang X, Song F, Zhang H, Shen D, Wang B 2019 Nat. Commun. 10 4469 Google Scholar
[117]	Chong S K, Lei C, Lee S H, Jaroszynski J, Mao Z, Macdonald A H, Wang K 2022 arXiv: 2208.13332v1 [cond-mat. mes-hall
[118]	Glazkova D A, Estyunin D A, Klimovskikh I I, Makarova T P, Tereshchenko O E, Kokh K A, Golyashov V A, Koroleva A V, Shikin A M 2022 JETP Lett. 115 286 Google Scholar
[119]	Liu Y, Wang L L, Zheng Q, Huang Z, Wang X, Chi M, Wu Y, Chakoumakos B C, McGuire M A, Sales B C, Wu W, Yan J 2021 Phys. Rev. X 11 021033 Google Scholar
[120]	Ge W, Sass P M, Yan J, Lee S H, Mao Z, Wu W 2021 Phys. Rev. B 103 134403 Google Scholar
[121]	Murakami T, Nambu Y, Koretsune T, Xiangyu G, Yamamoto T, Brown C M, Kageyama H 2019 Phys. Rev. B 100 195103 Google Scholar
[122]	Glazkova D A, Estyunin D A, Klimovskikh I I, Rybkina A A, Golovchanskiy I A, Tereshchenko O E, Kokh K A, Shchetinin I V, Golyashov V A, Shikin A M 2022 JETP Lett. 116 817 Google Scholar
[123]	Riberolles S X M, Zhang Q, Gordon E, Butch N P, Ke L, Yan J Q, McQueeney R J 2021 Phys. Rev. B 104 064401 Google Scholar
[124]	Yan J Q, Okamoto S, McGuire M A, May A F, McQueeney R J, Sales B C 2019 Phys. Rev. B 100 104409 Google Scholar
[125]	Lei C, Chen S, MacDonald A H 2020 Proc. Natl. Acad. Sci. U.S.A. 117 27224 Google Scholar
[126]	Wimmer S, Sánchez-Barriga J, Küppers P, Ney A, Schierle E, Freyse F, Caha O, Michalička J, Liebmann M, Primetzhofer D, Hoffman M, Ernst A, Otrokov M M, Bihlmayer G, Weschke E, Lake B, Chulkov E V, Morgenstern M, Bauer G, Springholz G, Rader O 2021 Adv. Mater. 33 2102935 Google Scholar
[127]	Lee S H, Graf D, Min L, Zhu Y, Yi H, Ciocys S, Wang Y, Choi E S, Basnet R, Fereidouni A, Wegner A, Zhao Y F, Verlinde K, He J, Redwing R, Gopalan V, Churchill H O H, Lanzara A, Samarth N, Chang C Z, Hu J, Mao Z Q 2021 Phys. Rev. X 11 031032 Google Scholar
[128]	Wang H H, Luo X G, Shi M Z, Peng K L, Lei B, Cui J H, Ma D H, Zhuo W Z, Ying J J, Wang Z Y, Chen X H 2021 Phys. Rev. B 103 085126 Google Scholar
[129]	Ma X M, Zhao Y, Zhang K, Kumar S, Lu R, Li J, Yao Q, Shao J, Hou F, Wu X, Zeng M, Hao Y J, Hao Z, Wang Y, Liu X R, Shen H, Sun H, Mei J, Miyamoto K, Okuda T, Arita M, Schwier E F, Shimada K, Deng K, Liu C, Lin J, Zhao Y, Chen C, Liu Q, Liu C 2021 Phys. Rev. B 103 L121112 Google Scholar
[130]	Lee S H, Zhu Y, Wang Y, Miao L, Pillsbury T, Yi H, Kempinger S, Hu J, Heikes C A, Quarterman P, Ratcliff W, Borchers J A, Zhang H, Ke X, Graf D, Alem N, Chang C Z, Samarth N, Mao Z 2019 Phys. Rev. Res. 1 012011 Google Scholar
[131]	Shikin A M, Estyunin D A, Klimovskikh I I, Filnov S O, Schwier E F, Kumar S, Miyamoto K, Okuda T, Kimura A, Kuroda K, Yaji K, Shin S, Takeda Y, Saitoh Y, Aliev Z S, Mamedov N T, Amiraslanov I R, Babanly M B, Otrokov M M, Eremeev S V, Chulkov E V 2020 Sci. Rep. 10 13226 Google Scholar
[132]	Vidal R C, Bentmann H, Peixoto T R F, Zeugner A, Moser S, Min C H, Schatz S, Kißner K, Ünzelmann M, Fornari C I, Vasili H B, Valvidares M, Sakamoto K, Mondal D, Fujii J, Vobornik I, Jung S, Cacho C, Kim T K, Koch R J, Jozwiak C, Bostwick A, Denlinger J D, Rotenberg E, Buck J, Hoesch M, Diekmann F, Rohlf S, Kalläne M, Rossnagel K, Otrokov M M, Chulkov E V, Ruck M, Isaeva A, Reinert F 2019 Phys. Rev. B 100 121104 Google Scholar
[133]	Chen Y J, Xu L X, Li J H, Li Y W, Wang H Y, Zhang C F, Li H, Wu Y, Liang A J, Chen C, Jung S W, Cacho C, Mao Y H, Liu S, Wang M X, Guo Y F, Xu Y, Liu Z K, Yang L X, Chen Y L 2019 Phys. Rev. X 9 041040 Google Scholar
[134]	Hao Y J, Liu P, Feng Y, Ma X M, Schwier E F, Arita M, Kumar S, Hu C, Lu R e, Zeng M, Wang Y, Hao Z, Sun H Y, Zhang K, Mei J, Ni N, Wu L, Shimada K, Chen C, Liu Q, Liu C 2019 Phys. Rev. X 9 041038 Google Scholar
[135]	Li H, Gao S Y, Duan S F, Xu Y F, Zhu K J, Tian S J, Gao J C, Fan W H, Rao Z C, Huang J R, Li J J, Yan D Y, Liu Z T, Liu W L, Huang Y B, Li Y L, Liu Y, Zhang G B, Zhang P, Kondo T, Shin S, Lei H C, Shi Y G, Zhang W T, Weng H M, Qian T, Ding H 2019 Phys. Rev. X 9 041039 Google Scholar
[136]	Swatek P, Wu Y, Wang L L, Lee K, Schrunk B, Yan J, Kaminski A 2020 Phys. Rev. B 101 161109 Google Scholar
[137]	Nevola D, Li H X, Yan J Q, Moore R G, Lee H N, Miao H, Johnson P D 2020 Phys. Rev. Lett. 125 117205 Google Scholar
[138]	Yang Z, Zhang H 2022 New J. Phys. 24 073034 Google Scholar
[139]	Yasuda K, Mogi M, Yoshimi R, Tsukazaki A, Takahashi K S, Kawasaki M, Kagawa F, Tokura Y 2017 Science 358 1311 Google Scholar
[140]	Garrity K F, Chowdhury S, Tavazza F M 2021 Phys. Rev. Mater. 5 024207 Google Scholar
[141]	Sass P M, Kim J, Vanderbilt D, Yan J, Wu W 2020 Phys. Rev. Lett. 125 037201 Google Scholar
[142]	Sass P M, Ge W, Yan J, Obeysekera D, Yang J J, Wu W 2020 Nano Lett. 20 2609 Google Scholar
[143]	Shikin A M, Estyunin D A, Zaitsev N L, Glazkova D, Klimovskikh I I, Filnov S O, Rybkin A G, Schwier E F, Kumar S, Kimura A, Mamedov N, Aliev Z, Babanly M B, Kokh K, Tereshchenko O E, Otrokov M M, Chulkov E V, Zvezdin K A, Zvezdin A K 2021 Phys. Rev. B 104 115168 Google Scholar
[144]	Lai Y, Ke L, Yan J, McDonald R D, McQueeney R J 2021 Phys. Rev. B 103 184429 Google Scholar
[145]	Garnica M, Otrokov M M, Aguilar P C, Klimovskikh I I, Estyunin D, Aliev Z S, Amiraslanov I R, Abdullayev N A, Zverev V N, Babanly M B, Mamedov N T, Shikin A M, Arnau A, de Parga A L V, Chulkov E V, Miranda R 2022 npj Quantum Mater. 7 7 Google Scholar
[146]	Ma X M, Chen Z, Schwier E F, Zhang Y, Hao Y J, Kumar S, Lu R, Shao J, Jin Y, Zeng M, Liu X R, Hao Z, Zhang K, Mansuer W, Song C, Wang Y, Zhao B, Liu C, Deng K, Mei J, Shimada K, Zhao Y, Zhou X, Shen B, Huang W, Liu C, Xu H, Chen C 2020 Phys. Rev. B 102 245136 Google Scholar
[147]	Wang D H, Wang H Q, Xing D Y, Zhang H J 2022 arXiv: 2205.08204v1 [cond-mat. mes-hall
[148]	Tan H, Yan B 2023 Phys. Rev. Lett. 130 126702 Google Scholar
[149]	Bai Y, Li Y, Luan J, Liu R, Song W, Chen Y, Ji P F, Zhang Q, Meng F, Tong B, Li L, Jiang Y, Gao Z, Gu L, Zhang J, Wang Y, Xue Q K, He K, Feng Y, Feng X 2022 arXiv: 2206.03773v2 [cond-mat. mes-hall
[150]	Liu S, Yu J, Zhang E, Li Z, Sun Q, Zhang Y, Li L, Zhao M, Leng P, Cao X, Zou J, Kou X, Zang J, Xiu F 2021 arXiv: 2110.00540v1 [cond-mat. mtrl-sci
[151]	Zhao Y F, Zhou L J, Wang F, Wang G, Song T, Ovchinnikov D, Yi H, Mei R, Wang K, Chan M H W, Liu C X, Xu X, Chang C Z 2021 Nano Lett. 21 7691 Google Scholar
[152]	Xu Y, Elcoro L, Song Z D, Wieder B J, Vergniory M G, Regnault N, Chen Y, Felser C, Bernevig B A 2020 Nature 586 702 Google Scholar
[153]	Su Y, Hu J, Cai X, Shi W, Xia Y, Xu Y, Xu X, Chen Y, Li G 2022 npj Comput. Mater. 8 261 Google Scholar
[154]	Choudhary K, Garrity K F, Ghimire N J, Anand N, Tavazza F 2021 Phys. Rev. B 103 155131 Google Scholar
[155]	Watanabe H, Po H C, Vishwanath A 2018 Sci. Adv. 4 eaat8685 Google Scholar
[156]	Elcoro L, Wieder B J, Song Z, Xu Y, Bradlyn B, Bernevig B A 2021 Nat. Commun. 12 5965 Google Scholar

施引文献

图 1 磁性拓扑绝缘体奇异拓扑性质及应用前景^[23]　(a) 量子反常霍尔效应^[9]; (b) 轴子绝缘体态^[24,25]; (c) 太赫兹辐射^[21]; (d) 手性马约拉纳费米子及拓扑量子计算^[26]

Fig. 1. Singular topological properties and application prospects of magnetic topological insulators^[23]: (a) Quantum anomalous Hall effect^[9]; (b) axion insulator state with antiparallel magnetization ^[24,25]; (c) terahertz radiation^[21]; (d) chiral Majorana fermions and topological quantum computation^[26].

下载: 全尺寸图片幻灯片

图 2 MBT的晶体结构图^[15,29]　(a) 由两个SLs组成反铁磁MBT的原子结构图^[15]. 每个SL内为铁磁性, 相邻SL之间为反铁磁性. 红色箭头表示Mn原子磁矩; 绿色箭头表示空间平移算符τ_1/2; (b) 在Si(111)衬底上生长的5 SLs MBT薄膜的横截面HAADF-STEM图像^[29]; (c) HAADF-STEM沿(b)中Cut 1的强度分布图^[29]; (d)在Si(111)上生长的MBT薄膜的XRD图^[29]

Fig. 2. Crystal structure in MBT^[15,29]: (a) Atomic structure of MBT consists of two SLs, whose magnetic states are ferromagnetic within each SL and antiferromagnetic between adjacent SLs^[15]. The red arrows represent the spin moment of Mn atom. The green arrow denotes for the half translation operator τ_1/2; (b) cross-sectional HAADF-STEM image of a 5 SLs MBT films grown on a Si(111) substrate^[29]; (c) intensity distribution of HAADF-STEM along Cut 1 in panel (b)^[29]; (d) XRD pattern of MBT films grown on Si(111)^[29].

下载: 全尺寸图片幻灯片

图 3 MBT磁相图　(a) MBT薄膜的层数-温度相图^[47]; PM代表顺磁区域; A-type AFM代表A型反铁磁区域; (b) 12 SLs MBT/Pt异质结自旋排列随温度和外加磁场的变化^[39]; (c) 2 SLs MBT的温度-磁场相图^[47]; (d) 3 SLs MBT的温度-磁场相图^[47]; 白色圆圈和三角形分别表示在不同温度下计算得到的spin-flop场μ₀H₁和spin-flip场μ₀H₂, 即A-AFM/CAFM相和CAFM/FM相的临界转变点; 实验数据点用灰色的球和三角形表示

Fig. 3. Magnetic phase diagram of MBT: (a) Layer number-temperature phase diagram of the MBT flake^[47]; PM denotes the region where the flake is paramagnetic; A-type AFM denotes the region where adjacent ferromagnetic SLs couple antiferromagnetically with each other; (b) spin configuration of 12 SLs MBT/Pt bilayer as functions of temperature and external magnetic field^[39]; (c) temperature-field phase diagram of 2 SLs MBT^[47]; (d) temperature-field phase diagram of 3 SLs MBT^[47]; the white circles and triangles represent the calculated spin-flop field μ₀H₁ and spin-flip field μ₀H₂, respectively, at various temperatures, showing the boundaries of the A-type AFM/CAFM phase and CAFM/FM phase; the experimental data points are represented using grey spheres and triangles with corresponding error bars.

下载: 全尺寸图片幻灯片

图 4 MBT表面态能带结构图　(a) 保留S对称性的表面具有无能隙的Dirac锥表面态示意图^[42]; (b) MBT(011)方向表面 (保持S对称性)的表面态^[15,42]; (c) 破坏S对称性的表面具有有能隙的Dirac锥表面态^[42]; (d) MBT (111)方向表面(破坏S对称性)的表面态^[15,42]

Fig. 4. Energy band structure of MBT with surface state: (a) The Dirac surface state is gapless due to the S symmetry^[42]; (b) the surface state on MBT(011) with S symmetry^[15,42]; (c) the Dirac surface state is fully gapped due to the S symmetry broken^[42]; (d) the surface state on MBT(111) without S symmetry^[15,42].

下载: 全尺寸图片幻灯片

图 5 MBT丰富的拓扑量子态　(a) MBT薄膜(2D)和块体(3D)在不同磁化状态下丰富的拓扑量子态. QAH, 量子反常霍尔态; AI, 轴子绝缘体; QSH, 量子自旋霍尔态; TI, 拓扑绝缘体; WSM, Weyl半金属; DSM, Dirac半金属^[16,48]. (b) MBT (110)面和 (111)面的无带隙和有带隙表面态能带结构^[16,48]

Fig. 5. Rich MBT topological quantum states. (a) MBT thin films (2D) and bulk (3D) have rich topological quantum states in different magnetic states. QAH, quantum anomalous Hall state; AI, axion insulator; QSH, quantum spin Hall state; TI, topological insulator; WSM, Weyl semimetal; DSM, Dirac semimetal^[16,48]. (b) Surface states of the MBT (110) and (111) surfaces, which are gapless and gapped, respectively^[16,48].

下载: 全尺寸图片幻灯片

图 6 MBT量子反常霍尔效应　(a) 磁性拓扑绝缘体中表面态有带隙的能带结构示意图^[24]; (b) 奇数层MBT本征量子反常霍尔绝缘体的示意图^[16]; (c) 5 SLs的MBT样品零磁场下的量子反常霍尔效应^[31]

Fig. 6. Quantum anomalous Hall effect of MBT: (a) Schematic diagram of the energy band structure with a band gap in the surface state in a magnetic topological insulator^[24]; (b) illustration of intrinsic QAH insulators in odd layers^[16]; (c) quantum anomalous Hall effect under zero magnetic field in 5 SLs MBT^[31].

下载: 全尺寸图片幻灯片

图 8 MBT轴子绝缘体态^[16,32]　(a) 偶数层MBT本征轴子绝缘体的示意图^[16]. 顶部和底部有带隙的表面具有半整数量子化的霍尔电导, 其符号在偶数层中相反, 导致C = 0; (b) 轴子绝缘态的ρ_xx和$ \dfrac{{\rm{d}}{\rho }_{yx}}{{\rm{d}}H} $与栅极电压的依赖关系^[32]; (c) 栅极电压V_g = 25 V时, 不同温度下纵向电阻率和霍尔电阻率随磁场强度的变化关系^[32]

Fig. 8. Axion insulator state in MBT^[16,32]: (a) Illustration of intrinsic axion insulators in even layers^[16]. The intrinsically gapped surfaces on the top and bottom sides have half-quantized Hall conductances, whose signs are opposite in even layers, leading to C = 0 ; (b) gate dependence of ρ_xx and $ \dfrac{{\rm{d}}{\rho }_{yx}}{{\rm{d}}H} $ in axion insulator state^[32]; (c) longitudinal and Hall resistivities versus magnetic field strength at various temperatures with gate voltage V_g = 25 V^[32].

下载: 全尺寸图片幻灯片

图 7 MBT高陈数陈绝缘体态　(a) 5 SLs MBT门电压调控的反常霍尔效应^[31]; (b) 5 SLs MBT的顶部和底部表面态的示意图^[31]; (c) 10 SLs MBT中C = 2的高陈数陈绝缘体态的R_yx和R_xx与磁场和温度间的关系^[33]; (d) 具有两个手性边缘态的高陈数陈绝缘态示意图; 灰色和绿色表示相邻SLs的MBT^[33]; (e) 铁磁 MBT能带结构示意图, 其为磁性Weyl 半金属^[33]; (f) 计算得到的MBT陈数随膜厚的变化函数^[33]

Fig. 7. High Chern number of Chern insulator MBT. (a) Anomalous Hall effect of 5 SLs MBT by gate voltage^[31]. (b) Schematic band diagrams for the top and bottom surface states of this fivelayer sample^[31]. (c) Temperature and magnetic field dependence of R_yx and R_xx in high-Chern-number Chern insulator states with C = 2 in 10 SLs MBT device^[33]. (d) Schematic of high-Chern-number Chern insulator states with two chiral edge states across the band gap; gray and green indicate adjacent MBT SLs^[33]. (e) Schematic diagram of band structure of the ferromagnetic MBT, which is a magnetic Weyl semimetal^[33]. (f) Chern number as a function of film thickness in MBT^[33].

下载: 全尺寸图片幻灯片

图 9 MBT马约拉纳特性　(a) 无自旋Kitaev一维p波超导紧束缚链^[69]; (b) 环上的拓扑p + ip超导体在其内外边界支持手性马约拉纳边缘模式^[74]; (c) 无自旋二维p+ip超导体^[75], 三维拓扑绝缘体靠近铁磁体(M↓)和超导体(S)时, 沿超导体和铁磁体边缘出现手性马约拉纳模式; (d) 在AFM TI和s波超导SC之间的界面边缘(灰色)的马约拉纳铰链模式(蓝色和红色箭头)^[19]; (e) MBT薄膜与顶部表面的s波超导SC耦合^[94]

Fig. 9. Majorana characteristics in MBT. (a) Sketch of Kitaev one-dimensional p-wave superconducting tight binding chain without spin^[69]. (b) The topological p + ip superconductor on an annulus supports chiral Majorana edge modes at its inner and outer boundaries^[74]. (c) Spin free two-dimensional p + ip superconductors^[75]. When the three-dimensional topological insulator is close to the ferromagnet (M↓) and superconductor (S), the chiral Majorana mode appears along the edge mode superconductor and ferromagnet. (d) Majorana hinge modes (blue and red arrows) at the interface edge (gray) between an AFM TI and an s-wave superconducting SC^[19]. (e) The MBT thin film is coupled to s-wave superconducting SC on the top surface^[94].

下载: 全尺寸图片幻灯片

图 10 (a) MnBi₂Te₄(Bi₂Te₃)_n^[95]和(b) MnBi₂Te₄(MnTe)_m^[96]的原子结构排列图

Fig. 10. Atomic structure of (a) MnBi₂Te₄(Bi₂Te₃)_n^[95] and (b) MnBi₂Te₄(MnTe)_m^[96] .

下载: 全尺寸图片幻灯片

图 11 (MnBi₂Te₄)_m(Bi₂Te₃)_n体系丰富的拓扑物相　(a) (MnBi₂Te₄)_m(Bi₂Te₃)_n体系拓扑相图^[114]. 灰色、黄色和蓝色分别代表平庸的绝缘体、量子自旋霍尔态和量子反常霍尔态; (b) Mn-Bi-Te体系随层间电子耦合和交换作用的不同展现丰富的拓扑物相^[115]

Fig. 11. Rich topological phase in (MnBi₂Te₄)_m(Bi₂Te₃)_n system: (a) Topological phase diagram in (MnBi₂Te₄)_m(Bi₂Te₃)_n system^[114]. Gray, yellow, and blue represent normal insulators, quantum spin Hall states, and quantum anomalous Hall states, respectively; (b) phase diagram of the multilayer topological heterostructure Mn-Bi-Te systems in terms of relative spacing and magnetization^[115]

下载: 全尺寸图片幻灯片

图 12 Mn(Bi_1–xSb_x)₂Te₄的丰富物理现象及能带结构　(a) Mn(Bi_1–xSb_x)₂Te₄的n-p载流子转变和拓扑相变图^[116]; (b) 不同Sb掺杂浓度的Mn(Bi_1–xSb_x)₂Te₄样品的ARPES测量的能带结构图^[116,129]

Fig. 12. Rich physical phenomena and band structure of Mn(Bi_1–xSb_x)₂Te₄: (a) n-p carrier transition and topological phase transition diagram of Mn(Bi_1–xSb_x)₂Te₄^[116]; (b) band structure diagram of ARPES measurement of Mn(Bi_1–xSb_x)₂Te₄ samples with different Sb doping concentrations^[116,129].

下载: 全尺寸图片幻灯片

map

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[2]	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
[3]	Fu L, Kane C L 2007 Phys. Rev. B 76 045302 Google Scholar
[4]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[5]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[6]	Pesin D, MacDonald A H 2012 Nat. Mater. 11 409 Google Scholar
[7]	Rajamathi C R, Gupta U, Kumar N, Yang H, Sun Y, Suss V, Shekhar C, Schmidt M, Blumtritt H, Werner P, Yan B H, Parkin S, Felser C, Rao C N R 2017 Adv. Mater. 29 1606202 Google Scholar
[8]	Kitaev A Y 2003 Ann. Phys. 303 2 Google Scholar
[9]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[10]	Chang C Z, Zhao W, Kim D Y, Zhang H, Assaf B A, Heiman D, Zhang S C, Liu C, Chan M H W, Moodera J S 2015 Nat. Mater. 14 473 Google Scholar
[11]	Mogi M, Kawamura M, Yoshimi R, Tsukazaki A, Kozuka Y, Shirakawa N, Takahashi K S, Kawasaki M, Tokura Y 2017 Nat. Mater. 16 516 Google Scholar
[12]	Xiao D, Jiang J, Shin J H, Wang W, Wang F, Zhao Y F, Liu C, Wu W, Chan M H W, Samarth N, Chang C Z 2018 Phys. Rev. Lett. 120 056801 Google Scholar
[13]	Lachman E O, Young A F, Richardella A, Cuppens J, Naren H R, Anahory Y, Meltzer A Y, Kandala A, Kempinger S, Myasoedov Y, Huber M E, Samarth N, Zeldov E 2015 Sci. Adv. 1 e1500740 Google Scholar
[14]	Otrokov M M, Menshchikova T V, Vergniory M G, Rusinov I P, Yu Vyazovskaya A, Koroteev Y M, Bihlmayer G, Ernst A, Echenique P M, Arnau A, Chulkov E V 2017 2D Mater. 4 025082 Google Scholar
[15]	Zhang D, Shi M, Zhu T, Xing D, Zhang H, Wang J 2019 Phys. Rev. Lett. 122 206401 Google Scholar
[16]	Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, Xu Y 2019 Sci. Adv. 5 eaaw5685 Google Scholar
[17]	Otrokov M M, Rusinov I P, Blanco-Rey M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, Chulkov E V 2019 Phys. Rev. Lett. 122 107202 Google Scholar
[18]	Qi X L, Hughes T L, Zhang S C 2008 Phys. Rev. B 78 195424 Google Scholar
[19]	Peng Y, Xu Y 2019 Phys. Rev. B 99 195431 Google Scholar
[20]	He Q L, Hughes T L, Armitage N P, Tokura Y, Wang K L 2022 Nat. Mater. 21 15 Google Scholar
[21]	Chen X, Wang H, Liu H, Wang C, Wei G, Fang C, Wang H, Geng C, Liu S, Li P, Yu H, Zhao W, Miao J, Li Y, Wang L, Nie T, Zhao J, Wu X 2022 Adv. Mater. 34 2106172 Google Scholar
[22]	Flensberg K, von Oppen F, Stern A 2021 Nat. Rev. Mater. 6 944 Google Scholar
[23]	Wang Y, Ma X M, Hao Z, Cai Y, Rong H, Zhang F, Chen W, Zhang C, Lin J, Zhao Y, Liu C, Liu Q, Chen C 2023 Natl. Sci. Rev. DOI: 10.1093/nsr/nwad066
[24]	Tokura Y, Yasuda K, Tsukazaki A 2019 Nat. Rev. Phys. 1 126 Google Scholar
[25]	Mogi M, Kawamura M, Tsukazaki A, Yoshimi R, Takahashi K S, Kawasaki M, Tokura Y 2017 Sci. Adv. 3 eaao1669 Google Scholar
[26]	Lian B, Sun X Q, Vaezi A, Qi X L, Zhang S C 2018 Proc. Natl. Acad. Sci. U. S. A. 115 10938 Google Scholar
[27]	Mong R S K, Essin A M, Moore J E 2010 Phys. Rev. B 81 245209 Google Scholar
[28]	Lee D S, Kim T H, Park C H, Chung C Y, Lim Y S, Seo W S, Park H H 2013 CrystEngComm 15 5532 Google Scholar
[29]	Gong Y, Guo J, Li J, Zhu K, Liao M, Liu X, Zhang Q, Gu L, Tang L, Feng X, Zhang D, Li W, Song C, Wang L, Yu P, Chen X, Wang Y, Yao H, Duan W, Xu Y, Zhang S C, Ma X, Xue Q K, He K 2019 Chin. Phys. Lett. 36 076801 Google Scholar
[30]	Otrokov M M, Klimovskikh I I, Bentmann H, Estyunin D, Zeugner A, Aliev Z S, Gass S, Wolter A U B, Koroleva A V, Shikin A M, Blanco-Rey M, Hoffmann M, Rusinov I P, Vyazovskaya A Y, Eremeev S V, Koroteev Y M, Kuznetsov V M, Freyse F, Sánchez-Barriga J, Amiraslanov I R, Babanly M B, Mamedov N T, Abdullayev N A, Zverev V N, Alfonsov A, Kataev V, Buchner B, Schwier E F, Kumar S, Kimura A, Petaccia L, Di Santo G, Vidal R C, Schatz S, Kissner K, Unzelmann M, Min C H, Moser S, Peixoto T R F, Reinert F, Ernst A, Echenique P M, Isaeva A, Chulkov E V 2019 Nature 576 416 Google Scholar
[31]	Deng Y, Yu Y, Shi M Z, Guo Z, Xu Z, Wang J, Chen X H, Zhang Y 2020 Science 367 895 Google Scholar
[32]	Liu C, Wang Y, Li H, Wu Y, Li Y, Li J, He K, Xu Y, Zhang J, Wang Y 2020 Nat. Mater. 19 522 Google Scholar
[33]	Ge J, Liu Y, Li J, Li H, Luo T, Wu Y, Xu Y, Wang J 2020 Natl. Sci. Rev. 7 1280 Google Scholar
[34]	Li Y, Liu C, Wang Y, Lian Z, Li H, Chun O, Zhang J, Wang Y 2021 arXiv: 2105.10390v1 [cond-mat. mtrl-sci
[35]	Liu C, Wang Y, Yang M, Mao J, Li H, Li Y, Li J, Zhu H, Wang J, Li L, Wu Y, Xu Y, Zhang J, Wang Y 2021 Nat. Commun. 12 4647 Google Scholar
[36]	Wu M, Tu D, Nie Y, Miao S, Gao W, Han Y, Zhu X, Zhou J, Ning W, Tian M 2022 Nano Lett. 22 73 Google Scholar
[37]	Gao A, Liu Y F, Hu C, Qiu J X, Tzschaschel C, Ghosh B, Ho S C, Bérubé D, Chen R, Sun H, Zhang Z, Zhang X Y, Wang Y X, Wang N, Huang Z, Felser C, Agarwal A, Ding T, Tien H J, Akey A, Gardener J, Singh B, Watanabe K, Taniguchi T, Burch K S, Bell D C, Zhou B B, Gao W, Lu H Z, Bansil A, Lin H, Chang T R, Fu L, Ma Q, Ni N, Xu S Y 2021 Nature 595 521 Google Scholar
[38]	Tai L, Chong S K, Zhang H, Zhang P, Deng P, Eckberg C, Qiu G, Dai B, He H, wu D, Xu S, Davydov A, Wang K 2021 arXiv: 2103.09878v1 [cond-mat. mtrl-sci
[39]	Ye C, Xie X, Lü W, Huang K, Yang A J, Jiang S, Liu X, Zhu D, Qiu X, Tong M, Zhou T, Hsu C H, Chang G, Lin H, Li P, Yang K, Wang Z, Jiang T, Renshaw Wang X 2022 Nano Lett. 22 1366 Google Scholar
[40]	Zhang Z, Wang N, Cao N, Wang A, Zhou X, Watanabe K, Taniguchi T, Yan B, Gao W B 2022 Nat. Commun. 13 6191 Google Scholar
[41]	Bartram F M, Leng Y C, Wang Y, Liu L, Chen X, Peng H, Li H, Yu P, Wu Y, Lin M L, Zhang J, Tan P H, Yang L 2022 npj Quantum Mater. 7 84 Google Scholar
[42]	占国慧, 王怀强, 张海军 2020 物理 49 817 Google Scholar Zhan G H, Wang H Q, Zhang H J 2020 Physics 49 817 Google Scholar
[43]	郭文锑, 黄璐, 许桂贵, 钟克华, 张健敏, 黄志高 2021 70 047101 Google Scholar Guo W T, Huang L, Xu G G, Zhong K H, Zhang J M, Huang Z G 2021 Acta Phys. Sin. 70 047101 Google Scholar
[44]	Wang Y, Zhang F, Zeng M, Sun H, Hao Z, Cai Y, Rong H, Zhang C, Liu C, Ma X, Wang L, Guo S, Lin J, Liu Q, Liu C, Chen C 2023 Front. Phys. 18 21304 Google Scholar
[45]	Li B, Yan J Q, Pajerowski D M, Gordon E, Nedić A M, Sizyuk Y, Ke L, Orth P P, Vaknin D, McQueeney R J 2020 Phys. Rev. Lett. 124 167204 Google Scholar
[46]	Yan J Q, Zhang Q, Heitmann T, Huang Z, Chen K Y, Cheng J G, Wu W, Vaknin D, Sales B C, McQueeney R J 2019 Phys. Rev. Mater. 3 064202 Google Scholar
[47]	Yang S, Xu X, Zhu Y, Niu R, Xu C, Peng Y, Cheng X, Jia X, Huang Y, Xu X, Lu J, Ye Y 2021 Phys. Rev. X 11 011003 Google Scholar
[48]	Wang P, Ge J, Li J, Liu Y, Xu Y, Wang J 2021 The Innovation 2 100098 Google Scholar
[49]	Li J, Wang C, Zhang Z, Gu B-L, Duan W, Xu Y 2019 Phys. Rev. B 100 121103 Google Scholar
[50]	Deng H, Chen Z, Wołoś A, Konczykowski M, Sobczak K, Sitnicka J, Fedorchenko I V, Borysiuk J, Heider T, Pluciński Ł, Park K, Georgescu A B, Cano J, Krusin-Elbaum L 2021 Nat. Phys. 17 36 Google Scholar
[51]	Fu H, Liu C X, Yan B 2020 Sci. Adv. 6 eaaz0948 Google Scholar
[52]	Gao R, Qin G, Qi S, Qiao Z, Ren W 2021 Phys. Rev. Mater. 5 114201 Google Scholar
[53]	Ying Z, Zhang S, Chen B, Jia B, Fei F, Zhang M, Zhang H, Wang X, Song F 2022 Phys. Rev. B 105 085412 Google Scholar
[54]	Nomura K, Nagaosa N 2011 Phys. Rev. Lett. 106 166802 Google Scholar
[55]	Li H, Jiang H, Chen C Z, Xie X C 2021 Phys. Rev. Lett. 126 156601 Google Scholar
[56]	Tse W K, MacDonald A H 2010 Phys. Rev. Lett. 105 057401 Google Scholar
[57]	Wu L, Salehi M, Koirala N, Moon J, Oh S, Armitage N P 2016 Science 354 1124 Google Scholar
[58]	Wang J, Lian B, Qi X L, Zhang S C 2015 Phys. Rev. B 92 081107 Google Scholar
[59]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
[60]	Wilczek F 1987 Phys. Rev. Lett. 58 1799 Google Scholar
[61]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[62]	Wang J 2020 Sci. Chin. -Phys. , Mech. Astron. 63 127031 Google Scholar
[63]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[64]	Qi X L, Hughes T L, Zhang S C 2010 Phys. Rev. B 82 184516 Google Scholar
[65]	't Hooft G 1976 Phys. Rev. D 14 3421 Google Scholar
[66]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[67]	Chen C, Jiang K, Zhang Y, Liu C, Liu Y, Wang Z, Wang J 2020 Nat. Phys. 16 536 Google Scholar
[68]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[69]	Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003 Google Scholar
[70]	Stone M, Roy R 2004 Phys. Rev. B 69 184511 Google Scholar
[71]	Wang M X, Liu C, Xu J P, Yang F, Miao L, Yao M Y, Gao C L, Shen C, Ma X, Chen X, Xu Z A, Liu Y, Zhang S C, Qian D, Jia J F, Xue Q K 2012 Science 336 52 Google Scholar
[72]	Fu L, Kane C L 2009 Phys. Rev. Lett. 102 216403 Google Scholar
[73]	Sau J D, Lutchyn R M, Tewari S, Das Sarma S 2010 Phys. Rev. Lett. 104 040502 Google Scholar
[74]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[75]	Akhmerov A R, Nilsson J, Beenakker C W J 2009 Phys. Rev. Lett. 102 216404 Google Scholar
[76]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[77]	Fu L, Kane C L 2009 Phys. Rev. B 79 161408 Google Scholar
[78]	Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G D, Ding H, Shin S 2018 Science 360 182 Google Scholar
[79]	Kong L, Zhu S, Papaj M, Chen H, Cao L, Isobe H, Xing Y, Liu W, Wang D, Fan P, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Gao H J, Ding H 2019 Nat. Phys. 15 1181 Google Scholar
[80]	König E J, Coleman P 2019 Phys. Rev. Lett. 122 207001 Google Scholar
[81]	Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T, Tamegai T 2019 Nat. Mater. 18 811 Google Scholar
[82]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[83]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[84]	Xu J P, Wang M X, Liu Z L, Ge J F, Yang X, Liu C, Xu Z A, Guan D, Gao C L, Qian D, Liu Y, Wang Q H, Zhang F C, Xue Q K, Jia J F 2015 Phys. Rev. Lett. 114 017001 Google Scholar
[85]	Sun H H, Zhang K W, Hu L H, Li C, Wang G Y, Ma H Y, Xu Z A, Gao C L, Guan D D, Li Y Y, Liu C, Qian D, Zhou Y, Fu L, Li S C, Zhang F C, Jia J F 2016 Phys. Rev. Lett. 116 257003 Google Scholar
[86]	何映萍, 洪健松, 刘雄军 2020 69 110302 Google Scholar He Y P, Hong J S, Liu X J 2020 Acta Phys. Sin. 69 110302 Google Scholar
[87]	Strübi G, Belzig W, Choi M S, Bruder C 2011 Phys. Rev. Lett. 107 136403 Google Scholar
[88]	Chung S B, Qi X L, Maciejko J, Zhang S C 2011 Phys. Rev. B 83 100512 Google Scholar
[89]	Wang J, Zhou Q, Lian B, Zhang S-C 2015 Phys. Rev. B 92 064520 Google Scholar
[90]	Maciejko J, Qi X L, Drew H D, Zhang S C 2010 Phys. Rev. Lett. 105 166803 Google Scholar
[91]	Wang J, Lian B, Zhang S C 2014 Phys. Rev. B 89 085106 Google Scholar
[92]	Yan Q, Li H, Zeng J, Sun Q F, Xie X C 2021 Commun. Phys. 4 239 Google Scholar
[93]	Zhang X, Liu F 2021 Phys. Rev. B 103 024405 Google Scholar
[94]	Chen L, Cao Z, He K, Liu X, Liu D E 2023 Phys. Rev. B 107 165405 Google Scholar
[95]	Klimovskikh I I, Otrokov M M, Estyunin D, Eremeev S V, Filnov S O, Koroleva A, Shevchenko E, Voroshnin V, Rybkin A G, Rusinov I P, Blanco-Rey M, Hoffmann M, Aliev Z S, Babanly M B, Amiraslanov I R, Abdullayev N A, Zverev V N, Kimura A, Tereshchenko O E, Kokh K A, Petaccia L, Di Santo G, Ernst A, Echenique P M, Mamedov N T, Shikin A M, Chulkov E V 2020 npj Quantum Mater. 5 54 Google Scholar
[96]	Chen P, Yao Q, Xu J, Sun Q, Grutter A J, Quarterman P, Balakrishnan P P, Kinane C J, Caruana A J, Langridge S, Li A, Achinuq B, Heppell E, Ji Y, Liu S, Cui B, Liu J, Huang P, Liu Z, Yu G, Xiu F, Hesjedal T, Zou J, Han X, Zhang H, Yang Y, Kou X 2023 Nat. Electron. 6 18 Google Scholar
[97]	Tian S, Gao S, Nie S, Qian Y, Gong C, Fu Y, Li H, Fan W, Zhang P, Kondo T, Shin S, Adell J, Fedderwitz H, Ding H, Wang Z, Qian T, Lei H 2020 Phys. Rev. B 102 035144 Google Scholar
[98]	Hu C, Ding L, Gordon K N, Ghosh B, Tien H-J, Li H, Linn A G, Lien S W, Huang C Y, Mackey S, Liu J, Reddy P V S, Singh B, Agarwal A, Bansil A, Song M, Li D, Xu S Y, Lin H, Cao H, Chang T R, Dessau D, Ni N 2020 Science advances 6 eaba4275 Google Scholar
[99]	Wu J, Liu F, Liu C, Wang Y, Li C, Lu Y, Matsuishi S, Hosono H 2020 Adv. Mater. 32 2001815 Google Scholar
[100]	Shi M Z, Lei B, Zhu C S, Ma D H, Cui J H, Sun Z L, Ying J J, Chen X H 2019 Phys. Rev. B 100 155144 Google Scholar
[101]	Ding L, Hu C, Ye F, Feng E, Ni N, Cao H 2020 Phys. Rev. B 101 020412 Google Scholar
[102]	Hu Y, Xu L, Shi M, Luo A, Peng S, Wang Z Y, Ying J J, Wu T, Liu Z K, Zhang C F, Chen Y L, Xu G, Chen X H, He J F 2020 Phys. Rev. B 101 161113 Google Scholar
[103]	Jo N H, Wang L L, Slager R J, Yan J, Wu Y, Lee K, Schrunk B, Vishwanath A, Kaminski A 2020 Phys. Rev. B 102 045130 Google Scholar
[104]	Zhang R X, Wu F, Das Sarma S 2020 Phys. Rev. Lett. 124 136407 Google Scholar
[105]	Yan J Q, Liu Y H, Parker D S, Wu Y, Aczel A A, Matsuda M, McGuire M A, Sales B C 2020 Phys. Rev. Mater. 4 054202 Google Scholar
[106]	Hu C, Gordon K N, Liu P, Liu J, Zhou X, Hao P, Narayan D, Emmanouilidou E, Sun H, Liu Y, Brawer H, Ramirez A P, Ding L, Cao H, Liu Q, Dessau D, Ni N 2020 Nat. Commun. 11 97 Google Scholar
[107]	Vidal R C, Zeugner A, Facio J I, Ray R, Haghighi M H, Wolter A U B, Corredor Bohorquez L T, Caglieris F, Moser S, Figgemeier T, Peixoto T R F, Vasili H B, Valvidares M, Jung S, Cacho C, Alfonsov A, Mehlawat K, Kataev V, Hess C, Richter M, Büchner B, van den Brink J, Ruck M, Reinert F, Bentmann H, Isaeva A 2019 Phys. Rev. X 9 041065 Google Scholar
[108]	He K 2020 npj Quantum Mater. 5 90 Google Scholar
[109]	Xie H K, Wang D H, Cai Z X, Chen B, Guo J W, Naveed M, Zhang S, Zhang M H, Wang X F, Fei F C, Zhang H J, Song F Q 2020 Appl. Phys. Lett. 116 221902 Google Scholar
[110]	Xu X, Yang S, Wang H, Guzman R, Gao Y, Zhu Y, Peng Y, Zang Z, Xi M, Tian S, Li Y, Lei H, Luo Z, Yang J, Wang Y, Xia T, Zhou W, Huang Y, Ye Y 2022 Nat. Commun. 13 7646 Google Scholar
[111]	Wu X, Li J, Ma X M, Zhang Y, Liu Y, Zhou C-S, Shao J, Wang Q, Hao Y J, Feng Y, Schwier E F, Kumar S, Sun H, Liu P, Shimada K, Miyamoto K, Okuda T, Wang K, Xie M, Chen C, Liu Q, Liu C, Zhao Y 2020 Phys. Rev. X 10 031013 Google Scholar
[112]	Rienks E D L, Wimmer S, Sánchez-Barriga J, Caha O, Mandal P S, Růžička J, Ney A, Steiner H, Volobuev V V, Groiss H, Albu M, Kothleitner G, Michalička J, Khan S A, Minár J, Ebert H, Bauer G, Freyse F, Varykhalov A, Rader O, Springholz G 2019 Nature 576 423 Google Scholar
[113]	Lu R, Sun H, Kumar S, Wang Y, Gu M, Zeng M, Hao Y J, Li J, Shao J, Ma X M, Hao Z, Zhang K, Mansuer W, Mei J, Zhao Y, Liu C, Deng K, Huang W, Shen B, Shimada K, Schwier E F, Liu C, Liu Q, Chen C 2021 Phys. Rev. X 11 011039 Google Scholar
[114]	Sun H, Xia B, Chen Z, Zhang Y, Liu P, Yao Q, Tang H, Zhao Y, Xu H, Liu Q 2019 Phys. Rev. Lett. 123 096401 Google Scholar
[115]	Gu M, Li J, Sun H, Zhao Y, Liu C, Liu J, Lu H, Liu Q 2021 Nat. Commun. 12 3524 Google Scholar
[116]	Chen B, Fei F, Zhang D, Zhang B, Liu W, Zhang S, Wang P, Wei B, Zhang Y, Zuo Z, Guo J, Liu Q, Wang Z, Wu X, Zong J, Xie X, Chen W, Sun Z, Wang S, Zhang Y, Zhang M, Wang X, Song F, Zhang H, Shen D, Wang B 2019 Nat. Commun. 10 4469 Google Scholar
[117]	Chong S K, Lei C, Lee S H, Jaroszynski J, Mao Z, Macdonald A H, Wang K 2022 arXiv: 2208.13332v1 [cond-mat. mes-hall
[118]	Glazkova D A, Estyunin D A, Klimovskikh I I, Makarova T P, Tereshchenko O E, Kokh K A, Golyashov V A, Koroleva A V, Shikin A M 2022 JETP Lett. 115 286 Google Scholar
[119]	Liu Y, Wang L L, Zheng Q, Huang Z, Wang X, Chi M, Wu Y, Chakoumakos B C, McGuire M A, Sales B C, Wu W, Yan J 2021 Phys. Rev. X 11 021033 Google Scholar
[120]	Ge W, Sass P M, Yan J, Lee S H, Mao Z, Wu W 2021 Phys. Rev. B 103 134403 Google Scholar
[121]	Murakami T, Nambu Y, Koretsune T, Xiangyu G, Yamamoto T, Brown C M, Kageyama H 2019 Phys. Rev. B 100 195103 Google Scholar
[122]	Glazkova D A, Estyunin D A, Klimovskikh I I, Rybkina A A, Golovchanskiy I A, Tereshchenko O E, Kokh K A, Shchetinin I V, Golyashov V A, Shikin A M 2022 JETP Lett. 116 817 Google Scholar
[123]	Riberolles S X M, Zhang Q, Gordon E, Butch N P, Ke L, Yan J Q, McQueeney R J 2021 Phys. Rev. B 104 064401 Google Scholar
[124]	Yan J Q, Okamoto S, McGuire M A, May A F, McQueeney R J, Sales B C 2019 Phys. Rev. B 100 104409 Google Scholar
[125]	Lei C, Chen S, MacDonald A H 2020 Proc. Natl. Acad. Sci. U.S.A. 117 27224 Google Scholar
[126]	Wimmer S, Sánchez-Barriga J, Küppers P, Ney A, Schierle E, Freyse F, Caha O, Michalička J, Liebmann M, Primetzhofer D, Hoffman M, Ernst A, Otrokov M M, Bihlmayer G, Weschke E, Lake B, Chulkov E V, Morgenstern M, Bauer G, Springholz G, Rader O 2021 Adv. Mater. 33 2102935 Google Scholar
[127]	Lee S H, Graf D, Min L, Zhu Y, Yi H, Ciocys S, Wang Y, Choi E S, Basnet R, Fereidouni A, Wegner A, Zhao Y F, Verlinde K, He J, Redwing R, Gopalan V, Churchill H O H, Lanzara A, Samarth N, Chang C Z, Hu J, Mao Z Q 2021 Phys. Rev. X 11 031032 Google Scholar
[128]	Wang H H, Luo X G, Shi M Z, Peng K L, Lei B, Cui J H, Ma D H, Zhuo W Z, Ying J J, Wang Z Y, Chen X H 2021 Phys. Rev. B 103 085126 Google Scholar
[129]	Ma X M, Zhao Y, Zhang K, Kumar S, Lu R, Li J, Yao Q, Shao J, Hou F, Wu X, Zeng M, Hao Y J, Hao Z, Wang Y, Liu X R, Shen H, Sun H, Mei J, Miyamoto K, Okuda T, Arita M, Schwier E F, Shimada K, Deng K, Liu C, Lin J, Zhao Y, Chen C, Liu Q, Liu C 2021 Phys. Rev. B 103 L121112 Google Scholar
[130]	Lee S H, Zhu Y, Wang Y, Miao L, Pillsbury T, Yi H, Kempinger S, Hu J, Heikes C A, Quarterman P, Ratcliff W, Borchers J A, Zhang H, Ke X, Graf D, Alem N, Chang C Z, Samarth N, Mao Z 2019 Phys. Rev. Res. 1 012011 Google Scholar
[131]	Shikin A M, Estyunin D A, Klimovskikh I I, Filnov S O, Schwier E F, Kumar S, Miyamoto K, Okuda T, Kimura A, Kuroda K, Yaji K, Shin S, Takeda Y, Saitoh Y, Aliev Z S, Mamedov N T, Amiraslanov I R, Babanly M B, Otrokov M M, Eremeev S V, Chulkov E V 2020 Sci. Rep. 10 13226 Google Scholar
[132]	Vidal R C, Bentmann H, Peixoto T R F, Zeugner A, Moser S, Min C H, Schatz S, Kißner K, Ünzelmann M, Fornari C I, Vasili H B, Valvidares M, Sakamoto K, Mondal D, Fujii J, Vobornik I, Jung S, Cacho C, Kim T K, Koch R J, Jozwiak C, Bostwick A, Denlinger J D, Rotenberg E, Buck J, Hoesch M, Diekmann F, Rohlf S, Kalläne M, Rossnagel K, Otrokov M M, Chulkov E V, Ruck M, Isaeva A, Reinert F 2019 Phys. Rev. B 100 121104 Google Scholar
[133]	Chen Y J, Xu L X, Li J H, Li Y W, Wang H Y, Zhang C F, Li H, Wu Y, Liang A J, Chen C, Jung S W, Cacho C, Mao Y H, Liu S, Wang M X, Guo Y F, Xu Y, Liu Z K, Yang L X, Chen Y L 2019 Phys. Rev. X 9 041040 Google Scholar
[134]	Hao Y J, Liu P, Feng Y, Ma X M, Schwier E F, Arita M, Kumar S, Hu C, Lu R e, Zeng M, Wang Y, Hao Z, Sun H Y, Zhang K, Mei J, Ni N, Wu L, Shimada K, Chen C, Liu Q, Liu C 2019 Phys. Rev. X 9 041038 Google Scholar
[135]	Li H, Gao S Y, Duan S F, Xu Y F, Zhu K J, Tian S J, Gao J C, Fan W H, Rao Z C, Huang J R, Li J J, Yan D Y, Liu Z T, Liu W L, Huang Y B, Li Y L, Liu Y, Zhang G B, Zhang P, Kondo T, Shin S, Lei H C, Shi Y G, Zhang W T, Weng H M, Qian T, Ding H 2019 Phys. Rev. X 9 041039 Google Scholar
[136]	Swatek P, Wu Y, Wang L L, Lee K, Schrunk B, Yan J, Kaminski A 2020 Phys. Rev. B 101 161109 Google Scholar
[137]	Nevola D, Li H X, Yan J Q, Moore R G, Lee H N, Miao H, Johnson P D 2020 Phys. Rev. Lett. 125 117205 Google Scholar
[138]	Yang Z, Zhang H 2022 New J. Phys. 24 073034 Google Scholar
[139]	Yasuda K, Mogi M, Yoshimi R, Tsukazaki A, Takahashi K S, Kawasaki M, Kagawa F, Tokura Y 2017 Science 358 1311 Google Scholar
[140]	Garrity K F, Chowdhury S, Tavazza F M 2021 Phys. Rev. Mater. 5 024207 Google Scholar
[141]	Sass P M, Kim J, Vanderbilt D, Yan J, Wu W 2020 Phys. Rev. Lett. 125 037201 Google Scholar
[142]	Sass P M, Ge W, Yan J, Obeysekera D, Yang J J, Wu W 2020 Nano Lett. 20 2609 Google Scholar
[143]	Shikin A M, Estyunin D A, Zaitsev N L, Glazkova D, Klimovskikh I I, Filnov S O, Rybkin A G, Schwier E F, Kumar S, Kimura A, Mamedov N, Aliev Z, Babanly M B, Kokh K, Tereshchenko O E, Otrokov M M, Chulkov E V, Zvezdin K A, Zvezdin A K 2021 Phys. Rev. B 104 115168 Google Scholar
[144]	Lai Y, Ke L, Yan J, McDonald R D, McQueeney R J 2021 Phys. Rev. B 103 184429 Google Scholar
[145]	Garnica M, Otrokov M M, Aguilar P C, Klimovskikh I I, Estyunin D, Aliev Z S, Amiraslanov I R, Abdullayev N A, Zverev V N, Babanly M B, Mamedov N T, Shikin A M, Arnau A, de Parga A L V, Chulkov E V, Miranda R 2022 npj Quantum Mater. 7 7 Google Scholar
[146]	Ma X M, Chen Z, Schwier E F, Zhang Y, Hao Y J, Kumar S, Lu R, Shao J, Jin Y, Zeng M, Liu X R, Hao Z, Zhang K, Mansuer W, Song C, Wang Y, Zhao B, Liu C, Deng K, Mei J, Shimada K, Zhao Y, Zhou X, Shen B, Huang W, Liu C, Xu H, Chen C 2020 Phys. Rev. B 102 245136 Google Scholar
[147]	Wang D H, Wang H Q, Xing D Y, Zhang H J 2022 arXiv: 2205.08204v1 [cond-mat. mes-hall
[148]	Tan H, Yan B 2023 Phys. Rev. Lett. 130 126702 Google Scholar
[149]	Bai Y, Li Y, Luan J, Liu R, Song W, Chen Y, Ji P F, Zhang Q, Meng F, Tong B, Li L, Jiang Y, Gao Z, Gu L, Zhang J, Wang Y, Xue Q K, He K, Feng Y, Feng X 2022 arXiv: 2206.03773v2 [cond-mat. mes-hall
[150]	Liu S, Yu J, Zhang E, Li Z, Sun Q, Zhang Y, Li L, Zhao M, Leng P, Cao X, Zou J, Kou X, Zang J, Xiu F 2021 arXiv: 2110.00540v1 [cond-mat. mtrl-sci
[151]	Zhao Y F, Zhou L J, Wang F, Wang G, Song T, Ovchinnikov D, Yi H, Mei R, Wang K, Chan M H W, Liu C X, Xu X, Chang C Z 2021 Nano Lett. 21 7691 Google Scholar
[152]	Xu Y, Elcoro L, Song Z D, Wieder B J, Vergniory M G, Regnault N, Chen Y, Felser C, Bernevig B A 2020 Nature 586 702 Google Scholar
[153]	Su Y, Hu J, Cai X, Shi W, Xia Y, Xu Y, Xu X, Chen Y, Li G 2022 npj Comput. Mater. 8 261 Google Scholar
[154]	Choudhary K, Garrity K F, Ghimire N J, Anand N, Tavazza F 2021 Phys. Rev. B 103 155131 Google Scholar
[155]	Watanabe H, Po H C, Vishwanath A 2018 Sci. Adv. 4 eaat8685 Google Scholar
[156]	Elcoro L, Wieder B J, Song Z, Xu Y, Bradlyn B, Bernevig B A 2021 Nat. Commun. 12 5965 Google Scholar

[1]	王玉, 梁钰林, 邢燕霞. 石墨烯中的拓扑安德森绝缘体相. , 2025, 74(4): 047301. doi: 10.7498/aps.74.20241031
[2]	蒋婧, 王小云, 孔鹏, 赵鹤平, 何兆剑, 邓科. 声学四极子拓扑绝缘体中的位错态. , 2024, 73(15): 154302. doi: 10.7498/aps.73.20240640
[3]	李锦芳, 何东山, 王一平. 一维耦合腔晶格中磁子-光子拓扑相变和拓扑量子态的调制. , 2024, 73(4): 044203. doi: 10.7498/aps.73.20231519
[4]	刘钊. 莫尔超晶格中的分数化拓扑量子态. , 2024, 73(20): 207303. doi: 10.7498/aps.73.20241029
[5]	张帅, 宋凤麒. 拓扑绝缘体中量子霍尔效应的研究进展. , 2023, 72(17): 177302. doi: 10.7498/aps.72.20230698
[6]	黄月蕾, 单寅飞, 杜灵杰, 杜瑞瑞. 拓扑激子绝缘体的实验进展. , 2023, 72(17): 177101. doi: 10.7498/aps.72.20230634
[7]	郑智勇, 陈立杰, 向吕, 王鹤, 王一平. 一维超导微波腔晶格中反旋波效应对拓扑相变和拓扑量子态的调制. , 2023, 72(24): 244204. doi: 10.7498/aps.72.20231321
[8]	刘畅, 王亚愚. 磁性拓扑绝缘体中的量子输运现象. , 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
[9]	王伟, 王一平. 一维超导传输线腔晶格中的拓扑相变和拓扑量子态的调制. , 2022, 71(19): 194203. doi: 10.7498/aps.71.20220675
[10]	郭文锑, 黄璐, 许桂贵, 钟克华, 张健敏, 黄志高. 本征磁性拓扑绝缘体MnBi₂Te₄电子结构的压力应变调控. , 2021, 70(4): 047101. doi: 10.7498/aps.70.20201237
[11]	严忠波. 高阶拓扑绝缘体和高阶拓扑超导体简介. , 2019, 68(22): 226101. doi: 10.7498/aps.68.20191101
[12]	刘畅, 刘祥瑞. 强三维拓扑绝缘体与磁性拓扑绝缘体的角分辨光电子能谱学研究进展. , 2019, 68(22): 227901. doi: 10.7498/aps.68.20191450
[13]	郝宁, 胡江平. 铁基超导中拓扑量子态研究进展. , 2018, 67(20): 207101. doi: 10.7498/aps.67.20181455
[14]	李兆国, 张帅, 宋凤麒. 拓扑绝缘体的普适电导涨落. , 2015, 64(9): 097202. doi: 10.7498/aps.64.097202
[15]	王青, 盛利. 磁场中的拓扑绝缘体边缘态性质. , 2015, 64(9): 097302. doi: 10.7498/aps.64.097302
[16]	关童, 滕静, 吴克辉, 李永庆. 拓扑绝缘体(Bi0.5Sb0.5)2Te3薄膜中的线性磁阻. , 2015, 64(7): 077201. doi: 10.7498/aps.64.077201
[17]	陈艳丽, 彭向阳, 杨红, 常胜利, 张凯旺, 钟建新. 拓扑绝缘体Bi2Se3中层堆垛效应的第一性原理研究. , 2014, 63(18): 187303. doi: 10.7498/aps.63.187303
[18]	李平原, 陈永亮, 周大进, 陈鹏, 张勇, 邓水全, 崔雅静, 赵勇. 拓扑绝缘体Bi2Te3的热膨胀系数研究. , 2014, 63(11): 117301. doi: 10.7498/aps.63.117301
[19]	丁玥, 沈洁, 庞远, 刘广同, 樊洁, 姬忠庆, 杨昌黎, 吕力. Bi2Te3拓扑绝缘体表面颗粒化铅膜诱导的超导邻近效应. , 2013, 62(16): 167401. doi: 10.7498/aps.62.167401
[20]	曾伦武, 张浩, 唐中良, 宋润霞. 拓扑绝缘体椭球粒子的电磁散射. , 2012, 61(17): 177303. doi: 10.7498/aps.61.177303

计量

文章访问数: 8583
PDF下载量: 672
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

本征磁性拓扑绝缘体MnBi₂Te₄研究进展