铁基超导中拓扑量子态研究进展

郝宁; 胡江平

doi:10.7498/aps.67.20181455

摘要

铁基超导体和拓扑量子材料是近年来凝聚态物理两个重要的前沿研究方向.铁基超导体中是否能衍生出非平庸的拓扑现象是一个非常有意义的问题.本文从晶体对称性、布里渊区高对称点附近的有效模型以及自旋轨道耦合相互作用三个方面具体分析了铁基超导的电子结构的基本特点.在此基础上，重点阐述铁基超导的正常态、临近超导的长程有序态以及超导态中非平庸的拓扑量子态是如何衍生的；具体介绍了相关的理论模型以及结果，回顾了相关的实验进展，展望了该领域的发展前景.

关键词:

Abstract

Iron-based superconductors and topological quantum states have been two important research frontiers in condensed matter physics in recent years. It is a very significant question whether the nontrivial topological phenomena can occur in iron-based superconductors. In this paper, the basic characteristics of the electronic structure of iron-based superconducting are analyzed from three aspects:crystal symmetry, effective model near the high symmetry points in Brillouin zone, and spin-orbit coupling interaction. On this basis, this paper focuses on how the nontrivial topological quantum states occur in the normal state, the states with long-range order near superconducting state and the superconducting state. Furthermore, the relevant theoretical models and results are introduced in detail, the related experimental progress is reviewed, and the development in this field is prospected.

Keywords:

作者及机构信息

郝宁¹,
胡江平^2,3

1.
中国科学院强磁场科学中心, 极端条件凝聚态物理安徽省重点实验室, 合肥 230031;

2.
中国科学院物理研究所, 北京凝聚态物理国家研究中心, 北京 100190;

3.
中国科学院大学, 卡弗里理论科学研究所, 北京 100190

通信作者: 郝宁, haon@hmfl.ac.cn;jphu@iphy.ac.cn ; 胡江平, haon@hmfl.ac.cn;jphu@iphy.ac.cn

基金项目: 国家重点研究发展计划（批准号：2015CB921300，2017YFA0303100，2017YFA0303201）、国家自然科学基金（批准号：11674331，11334012）、中国科学院百人计划基金和中国科学院先导项目（批准号：XDB07000000）资助的课题.

Authors and contacts

Hao Ning¹,
Hu Jiang-Ping^2,3

1.
Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China;

2.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

3.
Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Hao Ning, haon@hmfl.ac.cn;jphu@iphy.ac.cn ; Hu Jiang-Ping, haon@hmfl.ac.cn;jphu@iphy.ac.cn

Funds: Project supported by the National Key Research and Development Plan of China (Grant Nos. 2015CB921300, 2017YFA0303100, 2017YFA0303201), the National Natural Science Foundation of China (Grant Nos. 11674331, 11334012), the 100 Talents Project of Chinese Academy of Sciences, and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB07000000).

参考文献

[1]	Kamihara Y, Watanabe T, Hirano M, Hosono H 2008 J. Am. Chem. Soc. 130 3296
[2]	Guo J, Jin S, Wang G, Wang S, Zhu K, Zhou T, He M, Chen X 2010 Phys. Rev. B: Condens. Matter 82 180520
[3]	Wang Q Y, Li Z, Zhang W H, Zhang Z C, Zhang J S, Li W, Ding H, Ou Y B, Deng P, Chang K 2012 Chin. Phys. Lett. 29 037402
[4]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[5]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[6]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[7]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803
[8]	Knig M, Wiedmann S, Brne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[9]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
[10]	Chen Y, Analytis J G, Chu J H, Liu Z, Mo S K, Qi X L, Zhang H, Lu D, Dai X, Fang Z 2009 Science 325 178
[11]	Lee P A, Wen X G 2008 Phys. Rev. B: Condens. Matter 78 144517
[12]	Cvetkovic V, Vafek O 2013 Phys. Rev. B: Condens. Matter 88 134510
[13]	Lebgue S 2007 Phys. Rev. B: Condens. Matter 75 035110
[14]	Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004
[15]	Hao N, Hu J 2014 Phys. Rev. B: Condens. Matter 89 045144
[16]	Liu C X, Qi X L, Zhang H, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B: Condens. Matter 82 045122
[17]	Kreisel A, Wang Y, Maier T A, Hirschfeld P J, Scalapino D J 2013 Phys. Rev. B: Condens. Matter 88 094522
[18]	Tiago M L, Zhou Y, Alemany M M G, Saad Y, Chelikowsky J R 2006 Phys. Rev. Lett. 97 147201
[19]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[20]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[21]	Hao N, Hu J 2014 Phys. Rev. X 4 031053
[22]	Ge J F, Liu Z L, Liu C, Gao C L, Qian D, Xue Q K, Liu Y, Jia J F 2015 Nat. Mater. 14 285
[23]	He S, He J, Zhang W, Zhao L, Liu D, Liu X, Mou D, Ou Y B, Wang Q Y, Li Z 2013 Nat. Mater. 12 605
[24]	Tan S, Zhang Y, Xia M, Ye Z, Chen F, Xie X, Peng R, Xu D, Fan Q, Xu H 2013 Nat. Mater. 12 634
[25]	Liu D, Zhang W, Mou D, He J, Ou Y B, Wang Q Y, Li Z, Wang L, Zhao L, He S 2012 Nat. Commun. 3 931
[26]	Lee J, Schmitt F, Moore R, Johnston S, Cui Y T, Li W, Yi M, Liu Z, Hashimoto M, Zhang Y 2014 Nature 515 245
[27]	Miyata Y, Nakayama K, Sugawara K, Sato T, Takahashi T 2015 Nat. Mater. 14 775
[28]	Peng R, Xu H, Tan S, Cao H, Xia M, Shen X, Huang Z, Wen C, Song Q, Zhang T 2014 Nat. Commun. 5 5044
[29]	Hao N, Shen S Q 2015 Phys. Rev. B: Condens. Matter 92 165104
[30]	Fu L, Kane C L 2007 Phys. Rev. B: Condens. Matter 76 045302
[31]	Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B: Condens. Matter 81 115407
[32]	Liu K, Lu Z Y, Xiang T 2012 Phys. Rev. B: Condens. Matter 85 235123
[33]	Timur B, Marvin L C 2013 J. Phys.: Condens. Matter 25 105506
[34]	Zheng F, Wang Z, Kang W, Zhang P 2013 Sci. Rep. 3 2213
[35]	Wu X, Qin S, Liang Y, Fan H, Hu J 2016 Phys. Rev. B: Condens. Matter 93 115129
[36]	Margadonna S, Takabayashi Y, McDonald M T, Kasperkiewicz K, Mizuguchi Y, Takano Y, Fitch A N, Suard E, Prassides K 2008 Chem. Commun. 43 5607
[37]	Lehman M C, Llobet A, Horigane K, Louca D 2010 J. Phys. Conf. Ser. 251 012009
[38]	Imai Y, Sawada Y, Nabeshima F, Maeda A 2015 Proc. Natl. Acad. Sci. U. S. A. 112 1937
[39]	Wang Z, Zhang P, Xu G, Zeng L K, Miao H, Xu X, Qian T, Weng H, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B: Condens. Matter 92 115119
[40]	Li S, de la Cruz C, Huang Q, Chen Y, Lynn J W, Hu J, Huang Y L, Hsu F C, Yeh K W, Wu M K, Dai P 2009 Phys. Rev. B: Condens. Matter 79 054503
[41]	Phelan D, Millican J N, Thomas E L, Leo J B, Qiu Y, Paul R 2009 Phys. Rev. B: Condens. Matter 79 014519
[42]	Eschrig H, Koepernik K 2009 Phys. Rev. B: Condens. Matter 80 104503
[43]	Wu X, Qin S, Liang Y, Le C, Fan H, Hu J 2015 Phys. Rev. B: Condens. Matter 91 081111
[44]	Yakita H, Ogino H, Okada T, Yamamoto A, Kishio K, Tohei T, Ikuhara Y, Gotoh Y, Fujihisa H, Kataoka K, Eisaki H, Shimoyama J I 2014 J. Am. Chem. Soc. 136 846
[45]	Katayama N, Kudo K, Onari S, Mizukami T, Sugawara K, Sugiyama Y, Kitahama Y, Iba K, Fujimura K, Nishimoto N, Nohara M, Sawa H 2013 J. Phys. Soc. Jpn. 82 123702
[46]	Wu X, Le C, Liang Y, Qin S, Fan H, Hu J 2014 Phys. Rev. B: Condens. Matter 89 205102
[47]	Yu R, Qi X L, Bernevig A, Fang Z, Dai X 2011 Phys. Rev. B: Condens. Matter 84 075119
[48]	Borisenko S V, Evtushinsky D, Liu Z H, Morozov I, Kappenberger R, Wurmehl S, Bchner B, Yaresko A, Kim T, Hoesch M 2016 Nat. Phys. 12 311
[49]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801
[50]	Kim S H, Jin K H, Park J, Kim J S, Jhi S H, Kim T H, Yeom H W 2014 Phys. Rev. B: Condens. Matter 89 155436
[51]	Drozdov I K, Alexandradinata A, Jeon S, Nadj-Perge S, Ji H, Cava R J, Andrei Bernevig B, Yazdani A 2014 Nat. Phys. 10 664
[52]	Wang Z 2016 Nat. Mater. 15 968
[53]	Roth A, Brne C, Buhmann H, Molenkamp L W, Maciejko J, Qi X L, Zhang S C 2009 Science 325 294
[54]	Brne C, Liu C, Novik E, Hankiewicz E, Buhmann H, Chen Y, Qi X, Shen Z, Zhang S, Molenkamp L 2011 Phys. Rev. Lett. 106 126803
[55]	Shi X, Han Z Q, Richard P, Wu X X, Peng X L, Qian T, Wang S C, Hu J P, Sun Y J, Ding H 2017 Sci. Bull. 62 503
[56]	Liu Z H, Richard P, Xu N, Xu G, Li Y, Fang X C, Jia L L, Chen G F, Wang D M, He J B, Qian T, Hu J P, Ding H, Wang S C 2012 Phys. Rev. Lett. 109 037003
[57]	Huang D, Song C L, Webb T A, Fang S, Chang C Z, Moodera J S, Kaxiras E, Hoffman J E 2015 Phys. Rev. Lett. 115 017002
[58]	Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G, Ding H 2018 Science 360 182
[59]	Okazaki K, Ota Y, Kotani Y, Malaeb W, Ishida Y, Shimojima T, Kiss T, Watanabe S, Chen C T, Kihou K 2012 Science 337 1314
[60]	Yaji K, Harasawa A, Kuroda K, Toyohisa S, Nakayama M, Ishida Y, Fukushima A, Watanabe S, Chen C, Komori F 2016 Rev. Sci. Instrum. 87 053111
[61]	Liu Z T, Xing X Z, Li M Y, Zhou W, Sun Y, Fan C C, Yang H F, Liu J S, Yao Q, Li W, Shi Z X, Shen D W, Wang Z 2016 Appl. Phys. Lett. 109 042602
[62]	Fang C, Yao H, Tsai W F, Hu J, Kivelson S A 2008 Phys. Rev. B: Condens. Matter 77 224509
[63]	Xu C, Mller M, Sachdev S 2008 Phys. Rev. B: Condens. Matter 78 020501
[64]	Chu J, Kuo H 2012 Science 337 710
[65]	Fernandes R M, Chubukov A V, Schmalian J 2014 Nat. Phys. 10 97
[66]	Hu J, Xu B, Liu W, Hao N N, Wang Y 2012 Phys. Rev. B: Condens. Matter 85 144403
[67]	Chubukov A V, Fernandes R M, Schmalian J 2015 Phys. Rev. B: Condens. Matter 91 201105
[68]	Glasbrenner J, Mazin I, Jeschke H O, Hirschfeld P, Fernandes R, Valent R 2015 Nat. Phys. 11 953
[69]	Wang F, Kivelson S A, Lee D H 2015 Nat. Phys. 11 959
[70]	Yu R, Si Q 2015 Phys. Rev. Lett. 115 116401
[71]	Wang Q, Shen Y, Pan B, Hao Y, Ma M, Zhou F, Steffens P, Schmalzl K, Forrest T, Abdel-Hafiez M 2016 Nat. Mater. 15 159
[72]	Zhang P, Qian T, Richard P, Wang X, Miao H, Lv B, Fu B, Wolf T, Meingast C, Wu X 2015 Phys. Rev. B: Condens. Matter 91 214503
[73]	Zhang Y, Yi M, Liu Z, Li W, Lee J arXiv: 150301556[cond-mat.supr-con]
[74]	Mukherjee S, Kreisel A, Hirschfeld P, Andersen B M 2015 Phys. Rev. Lett. 115 026402
[75]	Watson M, Kim T, Haghighirad A, Davies N, McCollam A, Narayanan A, Blake S, Chen Y, Ghannadzadeh S, Schofield A 2015 Phys. Rev. B: Condens. Matter 91 155106
[76]	Tan S, Fang Y, Xie D, Feng W, Wen C, Song Q, Chen Q, Zhang W, Zhang Y, Luo L 2016 Phys. Rev. B: Condens. Matter 93 104513
[77]	Li W, Zhang Y, Lee J, Ding H, Yi M, Li Z, Deng P, Chang K, Mo S K, Hashimoto M 2015 arXiv:150901892[cond-mat.supr-con]
[78]	Wu X, Liang Y, Fan H, Hu J 2016 arXiv:160302055[cond-mat.supr-con]
[79]	Hu J, Yuan J 2016 Front. Phys. 11 117404
[80]	Jiang K, Hu J, Ding H, Wang Z 2016 Phys. Rev. B: Condens. Matter 93 115138
[81]	Hao N N, Wang Y P, Hu J P 2013 EPL 104 57007
[82]	Ran Y, Wang F, Zhai H, Vishwanath A, Lee D H 2009 Phys. Rev. B: Condens. Matter 79 014505
[83]	Park J, Friemel G, Li Y, Kim J H, Tsurkan V, Deisenhofer J, von Nidda H-A K, Loidl A, Ivanov A, Keimer B 2011 Phys. Rev. Lett. 107 177005
[84]	Hao N, Zheng F, Zhang P, Shen S Q 2017 Phys. Rev. B: Condens. Matter 96 165102
[85]	Mourik V, Zuo K, Frolov S M, Plissard S, Bakkers E P, Kouwenhoven L P 2012 Science 336 1003
[86]	Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602
[87]	Albrecht S M, Higginbotham A, Madsen M, Kuemmeth F, Jespersen T S, Nygrd J, Krogstrup P, Marcus C 2016 Nature 531 206
[88]	Xu S Y, Alidoust N, Belopolski I, Richardella A, Liu C, Neupane M, Bian G, Huang S H, Sankar R, Fang C 2014 Nat. Phys. 10 943
[89]	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
[90]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407
[91]	Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001
[92]	Yan B, Jansen M, Felser C 2013 Nat. Phys. 9 709
[93]	Alicea J 2012 Rep. Prog. Phys. 75 076501
[94]	Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001
[95]	Neupert T, Onoda S, Furusaki A 2010 Phys. Rev. Lett. 105 206404
[96]	Xu G, Lian B, Tang P, Qi X L, Zhang S C 2016 Phys. Rev. Lett. 117 047001
[97]	Yin J, Wu Z, Wang J, Ye Z, Gong J, Hou X, Shan L, Li A, Liang X, Wu X 2015 Nat. Phys. 11 543
[98]	Balatsky A, Vekhter I, Zhu J X 2006 Rev. Mod. Phys. 78 373
[99]	Pan S, Hudson E, Lang K, Eisaki H, Uchida S, Davis J 2000 Nature 403 746
[100]	Hudson E, Lang K, Madhavan V, Pan S, Eisaki H, Uchida S, Davis J 2001 Nature 411 920
[101]	Tsai W F, Zhang Y Y, Fang C, Hu J 2009 Phys. Rev. B: Condens. Matter 80 064513
[102]	Wang D, Kong L, Fan P, Chen H, Zhu S, Liu W, Cao L, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Ding H, Gao H J 2018 Science eaao1797

施引文献

[1]	Kamihara Y, Watanabe T, Hirano M, Hosono H 2008 J. Am. Chem. Soc. 130 3296
[2]	Guo J, Jin S, Wang G, Wang S, Zhu K, Zhou T, He M, Chen X 2010 Phys. Rev. B: Condens. Matter 82 180520
[3]	Wang Q Y, Li Z, Zhang W H, Zhang Z C, Zhang J S, Li W, Ding H, Ou Y B, Deng P, Chang K 2012 Chin. Phys. Lett. 29 037402
[4]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[5]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[6]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[7]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803
[8]	Knig M, Wiedmann S, Brne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[9]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
[10]	Chen Y, Analytis J G, Chu J H, Liu Z, Mo S K, Qi X L, Zhang H, Lu D, Dai X, Fang Z 2009 Science 325 178
[11]	Lee P A, Wen X G 2008 Phys. Rev. B: Condens. Matter 78 144517
[12]	Cvetkovic V, Vafek O 2013 Phys. Rev. B: Condens. Matter 88 134510
[13]	Lebgue S 2007 Phys. Rev. B: Condens. Matter 75 035110
[14]	Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004
[15]	Hao N, Hu J 2014 Phys. Rev. B: Condens. Matter 89 045144
[16]	Liu C X, Qi X L, Zhang H, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B: Condens. Matter 82 045122
[17]	Kreisel A, Wang Y, Maier T A, Hirschfeld P J, Scalapino D J 2013 Phys. Rev. B: Condens. Matter 88 094522
[18]	Tiago M L, Zhou Y, Alemany M M G, Saad Y, Chelikowsky J R 2006 Phys. Rev. Lett. 97 147201
[19]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[20]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[21]	Hao N, Hu J 2014 Phys. Rev. X 4 031053
[22]	Ge J F, Liu Z L, Liu C, Gao C L, Qian D, Xue Q K, Liu Y, Jia J F 2015 Nat. Mater. 14 285
[23]	He S, He J, Zhang W, Zhao L, Liu D, Liu X, Mou D, Ou Y B, Wang Q Y, Li Z 2013 Nat. Mater. 12 605
[24]	Tan S, Zhang Y, Xia M, Ye Z, Chen F, Xie X, Peng R, Xu D, Fan Q, Xu H 2013 Nat. Mater. 12 634
[25]	Liu D, Zhang W, Mou D, He J, Ou Y B, Wang Q Y, Li Z, Wang L, Zhao L, He S 2012 Nat. Commun. 3 931
[26]	Lee J, Schmitt F, Moore R, Johnston S, Cui Y T, Li W, Yi M, Liu Z, Hashimoto M, Zhang Y 2014 Nature 515 245
[27]	Miyata Y, Nakayama K, Sugawara K, Sato T, Takahashi T 2015 Nat. Mater. 14 775
[28]	Peng R, Xu H, Tan S, Cao H, Xia M, Shen X, Huang Z, Wen C, Song Q, Zhang T 2014 Nat. Commun. 5 5044
[29]	Hao N, Shen S Q 2015 Phys. Rev. B: Condens. Matter 92 165104
[30]	Fu L, Kane C L 2007 Phys. Rev. B: Condens. Matter 76 045302
[31]	Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B: Condens. Matter 81 115407
[32]	Liu K, Lu Z Y, Xiang T 2012 Phys. Rev. B: Condens. Matter 85 235123
[33]	Timur B, Marvin L C 2013 J. Phys.: Condens. Matter 25 105506
[34]	Zheng F, Wang Z, Kang W, Zhang P 2013 Sci. Rep. 3 2213
[35]	Wu X, Qin S, Liang Y, Fan H, Hu J 2016 Phys. Rev. B: Condens. Matter 93 115129
[36]	Margadonna S, Takabayashi Y, McDonald M T, Kasperkiewicz K, Mizuguchi Y, Takano Y, Fitch A N, Suard E, Prassides K 2008 Chem. Commun. 43 5607
[37]	Lehman M C, Llobet A, Horigane K, Louca D 2010 J. Phys. Conf. Ser. 251 012009
[38]	Imai Y, Sawada Y, Nabeshima F, Maeda A 2015 Proc. Natl. Acad. Sci. U. S. A. 112 1937
[39]	Wang Z, Zhang P, Xu G, Zeng L K, Miao H, Xu X, Qian T, Weng H, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B: Condens. Matter 92 115119
[40]	Li S, de la Cruz C, Huang Q, Chen Y, Lynn J W, Hu J, Huang Y L, Hsu F C, Yeh K W, Wu M K, Dai P 2009 Phys. Rev. B: Condens. Matter 79 054503
[41]	Phelan D, Millican J N, Thomas E L, Leo J B, Qiu Y, Paul R 2009 Phys. Rev. B: Condens. Matter 79 014519
[42]	Eschrig H, Koepernik K 2009 Phys. Rev. B: Condens. Matter 80 104503
[43]	Wu X, Qin S, Liang Y, Le C, Fan H, Hu J 2015 Phys. Rev. B: Condens. Matter 91 081111
[44]	Yakita H, Ogino H, Okada T, Yamamoto A, Kishio K, Tohei T, Ikuhara Y, Gotoh Y, Fujihisa H, Kataoka K, Eisaki H, Shimoyama J I 2014 J. Am. Chem. Soc. 136 846
[45]	Katayama N, Kudo K, Onari S, Mizukami T, Sugawara K, Sugiyama Y, Kitahama Y, Iba K, Fujimura K, Nishimoto N, Nohara M, Sawa H 2013 J. Phys. Soc. Jpn. 82 123702
[46]	Wu X, Le C, Liang Y, Qin S, Fan H, Hu J 2014 Phys. Rev. B: Condens. Matter 89 205102
[47]	Yu R, Qi X L, Bernevig A, Fang Z, Dai X 2011 Phys. Rev. B: Condens. Matter 84 075119
[48]	Borisenko S V, Evtushinsky D, Liu Z H, Morozov I, Kappenberger R, Wurmehl S, Bchner B, Yaresko A, Kim T, Hoesch M 2016 Nat. Phys. 12 311
[49]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801
[50]	Kim S H, Jin K H, Park J, Kim J S, Jhi S H, Kim T H, Yeom H W 2014 Phys. Rev. B: Condens. Matter 89 155436
[51]	Drozdov I K, Alexandradinata A, Jeon S, Nadj-Perge S, Ji H, Cava R J, Andrei Bernevig B, Yazdani A 2014 Nat. Phys. 10 664
[52]	Wang Z 2016 Nat. Mater. 15 968
[53]	Roth A, Brne C, Buhmann H, Molenkamp L W, Maciejko J, Qi X L, Zhang S C 2009 Science 325 294
[54]	Brne C, Liu C, Novik E, Hankiewicz E, Buhmann H, Chen Y, Qi X, Shen Z, Zhang S, Molenkamp L 2011 Phys. Rev. Lett. 106 126803
[55]	Shi X, Han Z Q, Richard P, Wu X X, Peng X L, Qian T, Wang S C, Hu J P, Sun Y J, Ding H 2017 Sci. Bull. 62 503
[56]	Liu Z H, Richard P, Xu N, Xu G, Li Y, Fang X C, Jia L L, Chen G F, Wang D M, He J B, Qian T, Hu J P, Ding H, Wang S C 2012 Phys. Rev. Lett. 109 037003
[57]	Huang D, Song C L, Webb T A, Fang S, Chang C Z, Moodera J S, Kaxiras E, Hoffman J E 2015 Phys. Rev. Lett. 115 017002
[58]	Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G, Ding H 2018 Science 360 182
[59]	Okazaki K, Ota Y, Kotani Y, Malaeb W, Ishida Y, Shimojima T, Kiss T, Watanabe S, Chen C T, Kihou K 2012 Science 337 1314
[60]	Yaji K, Harasawa A, Kuroda K, Toyohisa S, Nakayama M, Ishida Y, Fukushima A, Watanabe S, Chen C, Komori F 2016 Rev. Sci. Instrum. 87 053111
[61]	Liu Z T, Xing X Z, Li M Y, Zhou W, Sun Y, Fan C C, Yang H F, Liu J S, Yao Q, Li W, Shi Z X, Shen D W, Wang Z 2016 Appl. Phys. Lett. 109 042602
[62]	Fang C, Yao H, Tsai W F, Hu J, Kivelson S A 2008 Phys. Rev. B: Condens. Matter 77 224509
[63]	Xu C, Mller M, Sachdev S 2008 Phys. Rev. B: Condens. Matter 78 020501
[64]	Chu J, Kuo H 2012 Science 337 710
[65]	Fernandes R M, Chubukov A V, Schmalian J 2014 Nat. Phys. 10 97
[66]	Hu J, Xu B, Liu W, Hao N N, Wang Y 2012 Phys. Rev. B: Condens. Matter 85 144403
[67]	Chubukov A V, Fernandes R M, Schmalian J 2015 Phys. Rev. B: Condens. Matter 91 201105
[68]	Glasbrenner J, Mazin I, Jeschke H O, Hirschfeld P, Fernandes R, Valent R 2015 Nat. Phys. 11 953
[69]	Wang F, Kivelson S A, Lee D H 2015 Nat. Phys. 11 959
[70]	Yu R, Si Q 2015 Phys. Rev. Lett. 115 116401
[71]	Wang Q, Shen Y, Pan B, Hao Y, Ma M, Zhou F, Steffens P, Schmalzl K, Forrest T, Abdel-Hafiez M 2016 Nat. Mater. 15 159
[72]	Zhang P, Qian T, Richard P, Wang X, Miao H, Lv B, Fu B, Wolf T, Meingast C, Wu X 2015 Phys. Rev. B: Condens. Matter 91 214503
[73]	Zhang Y, Yi M, Liu Z, Li W, Lee J arXiv: 150301556[cond-mat.supr-con]
[74]	Mukherjee S, Kreisel A, Hirschfeld P, Andersen B M 2015 Phys. Rev. Lett. 115 026402
[75]	Watson M, Kim T, Haghighirad A, Davies N, McCollam A, Narayanan A, Blake S, Chen Y, Ghannadzadeh S, Schofield A 2015 Phys. Rev. B: Condens. Matter 91 155106
[76]	Tan S, Fang Y, Xie D, Feng W, Wen C, Song Q, Chen Q, Zhang W, Zhang Y, Luo L 2016 Phys. Rev. B: Condens. Matter 93 104513
[77]	Li W, Zhang Y, Lee J, Ding H, Yi M, Li Z, Deng P, Chang K, Mo S K, Hashimoto M 2015 arXiv:150901892[cond-mat.supr-con]
[78]	Wu X, Liang Y, Fan H, Hu J 2016 arXiv:160302055[cond-mat.supr-con]
[79]	Hu J, Yuan J 2016 Front. Phys. 11 117404
[80]	Jiang K, Hu J, Ding H, Wang Z 2016 Phys. Rev. B: Condens. Matter 93 115138
[81]	Hao N N, Wang Y P, Hu J P 2013 EPL 104 57007
[82]	Ran Y, Wang F, Zhai H, Vishwanath A, Lee D H 2009 Phys. Rev. B: Condens. Matter 79 014505
[83]	Park J, Friemel G, Li Y, Kim J H, Tsurkan V, Deisenhofer J, von Nidda H-A K, Loidl A, Ivanov A, Keimer B 2011 Phys. Rev. Lett. 107 177005
[84]	Hao N, Zheng F, Zhang P, Shen S Q 2017 Phys. Rev. B: Condens. Matter 96 165102
[85]	Mourik V, Zuo K, Frolov S M, Plissard S, Bakkers E P, Kouwenhoven L P 2012 Science 336 1003
[86]	Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602
[87]	Albrecht S M, Higginbotham A, Madsen M, Kuemmeth F, Jespersen T S, Nygrd J, Krogstrup P, Marcus C 2016 Nature 531 206
[88]	Xu S Y, Alidoust N, Belopolski I, Richardella A, Liu C, Neupane M, Bian G, Huang S H, Sankar R, Fang C 2014 Nat. Phys. 10 943
[89]	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
[90]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407
[91]	Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001
[92]	Yan B, Jansen M, Felser C 2013 Nat. Phys. 9 709
[93]	Alicea J 2012 Rep. Prog. Phys. 75 076501
[94]	Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001
[95]	Neupert T, Onoda S, Furusaki A 2010 Phys. Rev. Lett. 105 206404
[96]	Xu G, Lian B, Tang P, Qi X L, Zhang S C 2016 Phys. Rev. Lett. 117 047001
[97]	Yin J, Wu Z, Wang J, Ye Z, Gong J, Hou X, Shan L, Li A, Liang X, Wu X 2015 Nat. Phys. 11 543
[98]	Balatsky A, Vekhter I, Zhu J X 2006 Rev. Mod. Phys. 78 373
[99]	Pan S, Hudson E, Lang K, Eisaki H, Uchida S, Davis J 2000 Nature 403 746
[100]	Hudson E, Lang K, Madhavan V, Pan S, Eisaki H, Uchida S, Davis J 2001 Nature 411 920
[101]	Tsai W F, Zhang Y Y, Fang C, Hu J 2009 Phys. Rev. B: Condens. Matter 80 064513
[102]	Wang D, Kong L, Fan P, Chen H, Zhu S, Liu W, Cao L, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Ding H, Gao H J 2018 Science eaao1797

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