Majorana zero mode and its lattice construction in iron-based superconductors

Li Geng; Ding Hong; Wang Zi-Qiang; Gao Hong-Jun

doi:10.7498/aps.73.20232022

Abstract

Majorana zero modes (MZMs) obey non-Abelian braiding statistics. The braiding of MZMs can be used to construct the basic unit − topological qubit − of the topological quantum computation, which is immune to environmental noise and can achieve fault-tolerant quantum computation. The existing MZM platforms include hybrid structures such as topological insulator/superconductor, semiconducting nanowire/superconductor and 1d magnetic atomic chain/superconductor, and single materials such as 2M-WS₂, 4Hb-TaS₂, and iron-based superconductors (IBSs). The IBSs have advantages such as easy to fabricate, pure MZMs and high surviving temperatures of MZMs. Recently, a large-scale, ordered and tunable MZM lattice has been observed in LiFeAs, which provides a promising platform to future topological quantum computation. In this paper, first, we review the experimental observations of MZMs in IBSs, focusing on FeTe_0.55Se_0.45, (Li_0.84Fe_0.16)OHFeSe, CaKFe₄As₄ and LiFeAs. Next, we introduce the critical experimental evidences of the MZMs. We also review the recent research work on the ordered and tunable MZM lattice in LiFeAs. Finally, we give conclusion and perspective on future Majorana research.

Keywords:

Authors and contacts

1.
Nanoscale Physics and Devices Laboratory, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Hefei National Laboratory, Hefei 230088, China
4.
Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
5.
Boston College, Chestnut Hill, MA 02467, USA

Corresponding author: Gao Hong-Jun, hjgao@iphy.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2019YFA0308500, 2018YFA0305700), the National Natural Science Foundation of China (Grant Nos. 61888102, 51991340, 52072401), the Innovation Program of Quantum Science and Technology, China (Grant No. 2021ZD0302700), and the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-003).

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References

[1]	Majorana E 1937 Nuovo Ciment 14 171 Google Scholar
[2]	Avignone F T, Elliott S R, Engel J 2008 Rev. Mod. Phys. 80 481 Google Scholar
[3]	Arnquist I J, Avignone III F T, Barabash A S, Barton C J, Barton P J, Bhimani K H, Blalock E, Bos B, Busch M, Buuck M, Caldwell T S, Chan Y D, Christofferson C D, Chu P H, Clark M L, Cuesta C, Detwiler J A, Efremenko Yu, Ejiri H, Elliott S R, Giovanetti G K, Green M P, Gruszko J, Guinn I S, Guiseppe V E, Haufe C 3Lopez A M, López-Castàno J M, Martin E L, Martin R D, Massarczyk R, Meijer S J, Mertens S, Oli T K, Othman G, Paudel L S, Pettus W, Poon A W P, Radford D C, Reine A L, Rielage K, Ruof N W, Schaper D C, Tedeschi D, Varner R L, Vasilyev S, Wilkerson J F, Wiseman C, Xu W, Yu C H, Zhu B X 2023 Phys. Rev. Lett. 130 062501 Google Scholar
[4]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[5]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[6]	Kitaev A Y 2003 Ann. Phys-New. York. 303 2 Google Scholar
[7]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[8]	Aasen D, Hell M, Mishmash R V, Higginbotham A, Danon J, Leijnse M, Jespersen T S, Folk J A, Marcus C M, Flensberg K, Alicea J 2016 Phys. Rev. X 6 031016 Google Scholar
[9]	Moore G, Read N 1991 Nucl. Phys. B 360 362 Google Scholar
[10]	Read N, Green D 2000 Phys. Rev. B 61 10267 Google Scholar
[11]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[12]	Kitaev A Y 2001 Phys. Uspekhi 44 131 Google Scholar
[13]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[14]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[15]	Sau J D, Lutchyn R M, Tewari S, Das Sarma S 2010 Phys. Rev. Lett. 104 040502 Google Scholar
[16]	Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407 Google Scholar
[17]	Braunecker B, Simon P 2013 Phys. Rev. Lett. 111 147202 Google Scholar
[18]	Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805 Google Scholar
[19]	Li J, Neupert T, Wang Z J, MacDonald A H, Yazdani A, Bernevig B A 2016 Nat. Commun. 7 12297 Google Scholar
[20]	Maeno Y, Hashimoto H, Yoshida K, Nishizaki S, Fujita T, Bednorz J G, Lichtenberg F 1994 Nature 372 532 Google Scholar
[21]	Kallin C 2012 Rep. Prog. Phys. 75 042501 Google Scholar
[22]	Hassinger E, Bourgeois-Hope P, Taniguchi H, de Cotret S R, Grissonnanche G, Anwar M S, Maeno Y, Doiron-Leyraud N, Taillefer L 2017 Phys. Rev. X 7 011032 Google Scholar
[23]	Ran S, Eckberg C, Ding Q P, Furukawa Y, Metz T, Saha S R, Liu I L, Zic M, Kim H, Paglione J, Butch N P 2019 Science 365 684 Google Scholar
[24]	Jiao L, Howard S, Ran S, Wang Z Y, Rodriguez J O, Sigrist M, Wang Z Q, Butch N P, Madhavan V 2020 Nature 579 523 Google Scholar
[25]	Pustogow A, Luo Y K, Chronister A, Su Y S, Sokolov D A, Jerzembeck F, Mackenzie A P, Hicks C W, Kikugawa N, Raghu S, Bauer E D, Brown S E 2019 Nature 574 72 Google Scholar
[26]	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
[27]	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
[28]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[29]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[30]	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 Google Scholar
[31]	Ruby M, Pientka F, Peng Y, von Oppen F, Heinrich B W, Franke K J 2015 Phys. Rev. Lett. 115 197204 Google Scholar
[32]	Kim H, Palacio-Morales A, Posske T, Rozsa L, Palotas K, Szunyogh L, Thorwart M, Wiesendanger R 2018 Sci. Adv. 4 eaar5251 Google Scholar
[33]	Palacio-Morales A, Mascot E, Cocklin S, Kim H, Rachel S, Morr D K, Wiesendanger R 2019 Sci. Adv. 5 eaav6600 Google Scholar
[34]	Kezilebieke S, Huda M N, Vano V, Aapro M, Ganguli S C, Silveira O J, Glodzik S, Foster A S, Ojanen T, Liljeroth P 2020 Nature 588 424 Google Scholar
[35]	Kezilebieke S, Silveira O J, Huda M N, Vano V, Aapro M, Ganguli S C, Lahtinen J, Mansell R, van Dijken S, Foster A S, Liljeroth P 2021 Adv. Mater. 33 2006850 Google Scholar
[36]	Zheng H, Jia J F 2019 Chin. Phys. B 28 067403 Google Scholar
[37]	Chen M Y, Chen X Y, Yang H, Du Z Y, Wen H H 2018 Sci. Adv. 4 eaat1084 Google Scholar
[38]	Liang J, Zhang Y J, Yao X, Li H, Li Z X, Wang J N, Chen Y Z, Sou I K 2020 P. Natl. Acad. Sci. Usa. 117 221 Google Scholar
[39]	Jack B, Xie Y L, Yazdani A 2021 Nat. Rev. Phys. 3 541 Google Scholar
[40]	Yuan Y H, Pan J, Wang X T, Fang Y Q, Song C L, Wang L L, He K, Ma X C, Zhang H J, Huang F Q, Li W, Xue Q K 2019 Nat. Phys. 15 1046 Google Scholar
[41]	Nayak A K, Steinbok A, Roet Y, Koo J, Margalit G, Feldman I, Almoalem A, Kanigel A, Fiete G A, Yan B H, Oreg Y, Avraham N, Beidenkopf H 2021 Nat. Phys. 17 1413 Google Scholar
[42]	Lv Y F, Wang W L, Zhang Y M, Ding H, Li W, Wang L L, He K, Song C L, Ma X C, Xue Q K 2017 Sci. Bull. 62 852 Google Scholar
[43]	Wray L A, Xu S Y, Xia Y Q, Hor Y S, Qian D, Fedorov A V, Lin H, Bansil A, Cava R J, Hasan M Z 2010 Nat. Phys. 6 855 Google Scholar
[44]	Tao R, Yan Y J, Liu X, Wang Z W, Ando Y, Wang Q H, Zhang T, Feng D L 2018 Phys. Rev. X 8 041024 Google Scholar
[45]	Tanaka Y, Nakayama K, Souma S, Sato T, Xu N, Zhang P, Richard P, Ding H, Suzuki Y, Das P, Kadowaki K, Takahashi T 2012 Phys. Rev. B 85 125111 Google Scholar
[46]	Khim S, Landaeta J F, Banda J, Bannor N, Brando M, Brydon P M R, Hafner D, Kuchler R, Cardoso-Gil R, Stockert U, Mackenzie A P, Agterberg D F, Geibel C, Hassinger E 2021 Science 373 1012 Google Scholar
[47]	Landaeta J F, Khanenko P, Cavanagh D C, Geibel C, Khim S, Mishra S, Sheikin I, Brydon P M R, Agterberg D F, Brando M, Hassinger E 2022 Phys. Rev. X 12 031001 Google Scholar
[48]	Ortiz B R, Teicher S M L, Hu Y, Zuo J L, Sarte P M, Schueller E C, Abeykoon A M M, Krogstad M J, Rosenkranz S, Osborn R, Seshadri R, Balents L, He J F, Wilson S D 2020 Phys. Rev. Lett. 125 247002 Google Scholar
[49]	Chen H, Yang H T, Hu B, Zhao Z, Yuan J, Xing Y Q, Qian G J, Huang Z H, Li G, Ye Y H, Ma S, Ni S L, Zhang H, Yin Q W, Gong C S, Tu Z J, Lei H C, Tan H X, Zhou S, Shen C M, Dong X L, Yan B H, Wang Z Q, Gao H J 2021 Nature 599 222 Google Scholar
[50]	Liang Z W, Hou X Y, Zhang F, Ma W R, Wu P, Zhang Z Y, Yu F H, Ying J J, Jiang K, Shan L, Wang Z Y, Chen X H 2021 Phys. Rev. X 11 031026 Google Scholar
[51]	Paglione J, Greene R L 2010 Nat. Phys. 6 645 Google Scholar
[52]	Stewart G R 2011 Rev. Mod. Phys. 83 1589 Google Scholar
[53]	Wen H H, Li S L 2011 Annu. Rev. Condens. Matter Phys. 2 121 Google Scholar
[54]	Fernandes R M, Coldea A I, Ding H, Fisher I R, Hirschfeld P J, Kotliar G 2022 Nature 601 35 Google Scholar
[55]	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 362 333 Google Scholar
[56]	Li G, Zhu S Y, Wang D F, Wang Y L, Gao H J 2021 Supercond. Sci. Tech. 34 073001 Google Scholar
[57]	Li G, Zhu S Y, Fan P, Cao L, Gao H J 2022 Chin. Phys. B 31 080301 Google Scholar
[58]	Liu Q, Chen C, Zhang T, Peng R, Yan Y J, Wen C H P, Lou X, Huang Y L, Tian J P, Dong X L, Wang G W, Bao W C, Wang Q H, Yin Z P, Zhao Z X, Feng D L 2018 Phys. Rev. X 8 041056 Google Scholar
[59]	Liu W Y, Cao L, Zhu S Y, Kong L Y, Wang G W, Papaj M, Zhang P, Liu Y B, Chen H, Li G, Yang F Z, Kondo T, Du S X, Cao G H, Shin S, Fu L, Yin Z P, Gao H J, Ding H 2020 Nat. Commun. 11 5688 Google Scholar
[60]	Kong L Y, Cao L, Zhu S Y, Papaj M, Dai G Y, Li G, Fan P, Liu W Y, Yang F Z, Wang X C, Du S X, Jin C Q, Fu L, Gao H J, Ding H 2021 Nat. Commun. 12 4146 Google Scholar
[61]	Li M, Li G, Cao L, Zhou X T, Wang X C, Jin C Q, Chiu C K, Pennycook S J, Wang Z Q, Gao H J 2022 Nature 606 890 Google Scholar
[62]	Hao N N, Hu J P 2014 Phys. Rev. X 4 031053 Google Scholar
[63]	Hao N, Hu J P 2019 Natl. Sci. Rev. 6 213 Google Scholar
[64]	Wang Z J, Zhang P, Xu G, Zeng L K, Miao H, Xu X Y, Qian T, Weng H M, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B 92 115119 Google Scholar
[65]	Fang M H, Pham H M, Qian B, Liu T J, Vehstedt E K, Liu Y, Spinu L, Mao Z Q 2008 Phys. Rev. B 78 224503 Google Scholar
[66]	Chen G F, Chen Z G, Dong J, Hu W Z, Li G, Zhang X D, Zheng P, Luo J L, Wang N L 2009 Phys. Rev. B 79 140509(R Google Scholar
[67]	Pourret A, Malone L, Antunes A B, Yadav C S, Paulose P L, Fauque B, Behnia K 2011 Phys. Rev. B 83 020504(R Google Scholar
[68]	Homes C C, Dai Y M, Wen J S, Xu Z J, Gu G D 2015 Phys. Rev. B 91 144503 Google Scholar
[69]	Xu G, Lian B, Tang P Z, Qi X L, Zhang S C 2016 Phys. Rev. Lett. 117 047001 Google Scholar
[70]	Zhang Z Y 2017 Sci. Bull. 62 671 Google Scholar
[71]	Qin W, Gao J Q, Cui P, Zhang Z Y 2023 Sci. China-Phys. Mech. Astron. 66 267005 Google Scholar
[72]	Yazdani A, von Oppen F, Halperin B I, Yacoby A 2023 Science 380 eade0850 Google Scholar
[73]	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
[74]	Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T, Tamegai T 2019 Nat. Mater. 18 811 Google Scholar
[75]	Chiu C K, Machida T, Huang Y Y, Hanaguri T, Zhang F C 2020 Sci. Adv. 6 eaay0443 Google Scholar
[76]	Lu X F, Wang N Z, Wu H, Wu Y P, Zhao D, Zeng X Z, Luo X G, Wu T, Bao W, Zhang G H, Huang F Q, Huang Q Z, Chen X H 2015 Nat. Mater. 14 325 Google Scholar
[77]	Huang Y L, Feng Z P, Ni S L, Li J, Hu W, Liu S B, Mao Y Y, Zhou H X, Zhou F, Jin K, Wang H B, Yuan J, Dong X L, Zhao Z X 2017 Chin. Phys. Lett. 34 077404 Google Scholar
[78]	Hayashi N, Isoshima T, Ichioka M, Machida K 1998 Phys. Rev. Lett. 80 2921 Google Scholar
[79]	Khaymovich I M, Kopnin N B, Mel'nikov A S, Shereshevskii I A 2009 Phys. Rev. B 79 224506 Google Scholar
[80]	Hu L H, Li C, Xu D H, Zhou Y, Zhang F C 2016 Phys. Rev. B 94 224501 Google Scholar
[81]	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
[82]	Chen C, Liu Q, Zhang T Z, Li D, Shen P P, Dong X L, Zhao Z X, Zhang T, Feng D L 2019 Chin. Phys. Lett. 36 057403 Google Scholar
[83]	Cao L, Song Y, Liu Y B, Zheng Q, Han G Y, Liu W Y, Li M, Chen H, Xing Y Q, Cao G H, Ding H, Lin X, Du S X, Zhang Y Y, Li G, Wang Z Q, Gao H J 2021 Nano Res. 14 3921 Google Scholar
[84]	Iyo A, Kawashima K, Kinjo T, Nishio T, Ishida S, Fujihisa H, Gotoh Y, Kihou K, Eisaki H, Yoshida Y 2016 J. Am. Chem. Soc. 138 3410 Google Scholar
[85]	Kawakami T, Hu X 2015 Phys. Rev. Lett. 115 177001 Google Scholar
[86]	Wang X C, Liu Q Q, Lv Y X, Gao W B, Yang L X, Yu R C, Li F Y, Jin C Q 2008 Solid State Commun. 148 538 Google Scholar
[87]	Yin J X, Zhang S S, Dai G Y, Zhao Y Y, Kreisel A, Macam G, Wu X X, Miao H, Huang Z Q, Martiny J H J, Andersen B M, Shumiya N, Multer D, Litskevich M, Cheng Z J, Yang X, Cochran T A, Chang G Q, Belopolski I, Xing L Y, Wang X C, Gao Y, Chuang F C, Lin H, Wang Z Q, Jin C Q, Bang Y, Hasan M Z 2019 Phys. Rev. Lett. 123 217004 Google Scholar
[88]	Zhang P, Wang Z J, Wu X X, Yaji K, Ishida Y, Kohama Y, Dai G Y, Sun Y, Bareille C, Kuroda K, Kondo T, Okazaki K, Kindo K, Wang X C, Jin C Q, Hu J P, Thomale R, Sumida K, Wu S L, Miyamoto K, Okuda T, Ding H, Gu G D, Tamegai T, Kawakami T, Sato M, Shin S 2019 Nat. Phys. 15 41 Google Scholar
[89]	Hanaguri T, Kitagawa K, Matsubayashi K, Mazaki Y, Uwatoko Y, Takagi H 2012 Phys. Rev. B 85 214505 Google Scholar
[90]	Hu L H, Wu X X, Liu C X, Zhang R X 2022 Phys. Rev. Lett. 129 277001 Google Scholar
[91]	Konig E J, Coleman P 2019 Phys. Rev. Lett. 122 207001 Google Scholar
[92]	Qin S S, Hu L H, Le C C, Zeng J F, Zhang F C, Fang C, Hu J P 2019 Phys. Rev. Lett. 123 027003 Google Scholar
[93]	Chen C, Jiang K, Zhang Y, Liu C F, Liu Y, Wang Z Q, Wang J 2020 Nat. Phys. 16 536 Google Scholar
[94]	Zhang Y, Jiang K, Zhang F C, Wang J, Wang Z Q 2021 Phys. Rev. X 11 011041 Google Scholar
[95]	Yin J X, Wu Z, Wang J H, Ye Z Y, Gong J, Hou X Y, Shan L, Li A, Liang X J, Wu X X, Li J, Ting C S, Wang Z Q, Hu J P, Hor P H, Ding H, Pan S H 2015 Nat. Phys. 11 543 Google Scholar
[96]	Fan P, Yang F Z, Qian G J, Chen H, Zhang Y Y, Li G, Huang Z H, Xing Y Q, Kong L Y, Liu W Y, Jiang K, Shen C M, Du S X, Schneeloch J, Zhong R D, Gu G D, Wang Z Q, Ding H, Gao H J 2021 Nat. Commun. 12 1348 Google Scholar
[97]	Wang Z Y, Rodriguez J O, Jiao L, Howard S, Graham M, Gu G D, Hughes T L, Morr D K, Madhavan V 2020 Science 367 104 Google Scholar
[98]	Hu J P 2013 Phys. Rev. X 3 031004 Google Scholar
[99]	Hao N N, Hu J P 2014 Phys. Rev. B 89 045144 Google Scholar
[100]	Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001 Google Scholar
[101]	Zhu S, Kong L, Cao L, Chen H, Papaj M, Du S, Xing Y, Liu W, Wang D, Shen C, Yang F, Schneeloch J, Zhong R, Gu G, Fu L, Zhang Y Y, Ding H, Gao H J 2020 Science 367 189 Google Scholar
[102]	Ge J F, Bastiaans K M, Chatzopoulos D, Cho D, Tromp W O, Benschop T, Niu J, Gu G, Allan M P 2022 arXiv: 2205.10346 [cond-mat.supr-con
[103]	于渌 1965 物理学报 21 75 Google Scholar Yu L 1965 Acta Phys. Sin. 21 75 Google Scholar
[104]	Shiba H 1968 Prog. Theor. Phys. 40 435 Google Scholar
[105]	Rusinov A I 1969 JETP Lett. 9 1101
[106]	Caroli C, De Gennes P G, Matricon J 1964 Phys. Lett. 9 307 Google Scholar
[107]	Jeon S, Xie Y L, Li J, Wang Z J, Bernevig B A, Yazdani A 2017 Science 358 772 Google Scholar
[108]	Wang D F, Wiebe J, Zhong R D, Gu G D, Wiesendanger R 2021 Phys. Rev. Lett. 126 076802 Google Scholar
[109]	Cao L, Liu W Y, Li G, Dai G Y, Zheng Q, Wang Y X, Jiang K, Zhu S Y, Huang L, Kong L Y, Yang F Z, Wang X C, Zhou W, Lin X, Hu J P, Jin C Q, Ding H, Gao H J 2021 Nat. Commun. 12 6312 Google Scholar
[110]	Yim C M, Trainer C, Aluru R, Chi S, Hardy W N, Liang R X, Bonn D, Wahl P 2018 Nat. Commun. 9 2602 Google Scholar
[111]	Bonderson P, Freedman M, Nayak C 2009 Ann. Phys-new. York. 324 787 Google Scholar
[112]	Wang Y X, Lin M, Hughes T L 2018 Phys. Rev. B 98 165144 Google Scholar
[113]	Wang Q Y, Liu C C, Lu Y M, Zhang F 2018 Phys. Rev. Lett. 121 186801 Google Scholar
[114]	Hsu C H, Stano P, Klinovaja J, Loss D 2018 Phys. Rev. Lett. 121 196801 Google Scholar
[115]	Li C, Luo X J, Chen L, Liu D E, Zhang F C, Liu X 2022 Natl. Sci. Rev. 9 nwac095 Google Scholar

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图 1 (a) FeTe_0.55Se_0.45的高分辨扫描隧道显微镜(STM)图像; (b) 0.5 T下FeTe_0.55Se_0.45表面零偏压dI/dV map 图像; (c)单个磁通涡旋的零偏压dI/dV map 图像; (d)在磁通涡旋中心(红色)以及边界(黑色)处的dI/dV 谱线; (e)沿图(c)箭头方向的空间分辨dI/dV 谱线^[55]

Figure 1. (a) High-resolution scanning tunneling microscope (STM) topography of FeTe_0.55Se_0.45; (b) large-scale dI/dV map of FeTe_0.55Se_0.45 surface at 0 meV under 0.5 T; (c) dI/dV map of a typical vortex hosting MZM at 0 meV; (d) dI/dV curves taken at the center (red) and at the edge (black) of the vortex in panel (c); (e) a waterfall like plot of dI/dV line-cut along the dashed arrow in panel (c), the black curve corresponds to vortex center^[55].

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图 2 (a) DFT+DMFT计算得到的CaKFe₄As₄能带结构; (b) Γ—M方向的ARPES能谱图像; (c)对称化的EDC能谱曲线; (d) CaKFe₄As₄的STM形貌图; (e)一个涡旋附近的零偏压dI/dV map图像; (f)涡旋附近不同位置的dI/dV谱线比较; (g)不同涡旋束缚态的空间分布图案^[59]

Figure 2. (a) DFT+DMFT calculation results for the band structures of CaKFe₄As₄; (b) ARPES spectral intensity plots along the Γ–M direction on CaKFe₄As₄; (c) symmetrized EDCs at the momentum points marked by the red arrows in panel (b), the superconducting gap values of 5.9 meV is attributed to the topological surface bands; (d) STM topography of CaKFe₄As₄; (e) zero-bias conductance map around a vortex core; (f) comparison of dI/dV spectra at vortex core (P1), middle (P2), edge (P3), and without magnetic field (SC gap); (g) spatial patterns of vortex-bound states at energies corresponding to L₀ (MZM), L_–1, L_–2, and L_–3^[59].

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图 3 (a) Li(Fe, Co)As的晶格结构与布里渊区; (b) LiFeAs的能带结构示意图; (c) LiFeAs涡旋内部(红色)和外部(黑色)的大范围dI/dV 谱线; (d)跨越一个杂质辅助涡旋的大范围dI/dV谱线图, 显示出杂质的电子掺杂效应; (e)一个杂质辅助涡旋的零偏压dI/dV map图像; (f)图(e)中沿箭头方向的空间分辨dI/dV 谱线图^[60]

Figure 3. (a) Crystal structure and Brillouin zone of Li(Fe, Co)As; (b) LiFeAs band dispersion along Γ–M and Γ–Z; (c) wide range dI/dV spectra measured at an impurity assisted vortex (red curve) and on a clean surface region without impurities (black curve); (d) wide range line-cut intensity plot for an impurity assisted vortex, showing electron doping effect; (e) a zero bias conductance map around an impurity assisted vortex; (f) dI/dV intensity measured under 2.0 T along the white dashed line indicated in panel (e)^[60].

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图 4 (a) Fe原子沉积在FeTe_0.55Se_0.45表面的STM图像; (b)跨过一个Fe原子的空间分辨dI/dV 谱线图; (c), (d)在一个Fe原子上的dI/dV 谱线图随隧穿势垒的变化; (e), (f)在外加2 T磁场下, 一个Fe原子上的dI/dV 谱线图随隧穿势垒的变化^[96]

Figure 4. (a) STM image of FeTe_0.55Se_0.45 after atomic Fe atom deposition; (b) intensity plot of a series of spectra detected across Fe adatom; (c), (d) tunnel-barrier conductance dependence of the dI/dV spectra on a Fe atom and its intensity plots; (e), (f) the same as panel (c) and (d), but measured under a magnetic field of 6 T^[96].

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图 5 (a)跨越拓扑磁通涡旋的空间分辨dI/dV 谱线图; (b)跨越平庸磁通涡旋的空间分辨dI/dV 谱线图; (c) 35个拓扑磁通涡旋的涡旋束缚态能量统计图; (d) 26个平庸磁通涡旋的涡旋束缚态能量统计图^[81]

Figure 5. (a) Intensity plot and waterfall plot of a dI/dV linecut through a topological vortex core, showing the integer quantized vortex bond states; (b) the intensity plot and waterfall plot of a dI/dV linecut through an trivial vortex core, showing the half-odd-integer quantized vortex bond states; (c) a histogram of averaged level energies for 35 topological vortices; (d) a histogram of averaged level energies for 26 ordinary vortices^[81].

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图 6 (a)利用隧穿势垒调节耦合强度实验的示意图; (b)在不同的隧穿电导G_N下磁通涡旋中心的dI/dV谱线图; (c)不同能量下微分电导随隧穿势垒的变化的三维视觉图像; (d), (e)不同能量下微分电导随隧穿势垒变化的轮廓曲线^[101]

Figure 6. (a) Schematic of tunnel-coupling tunable experiment; Inset: dI/dV spectrum measured at vortex center under 2 T; (b) an overlapping plot of dI/dV spectra at vortex center under different G_N; (c) a three-dimensional schematic diagram depicting the variation in differential conductance values with respect to changes in energy and tunnel junction; (d) line profile of panel (c) along the dashed line at zero bias; (e) line profile of panel (c) along the dashed lines at high bias values^[101].

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图 7 (a)第一类褶皱的STM图像和高度曲线; (b)第二类褶皱的STM图像和高度曲线; (c)两类褶皱与正常区域处dI/dV谱线的比较; (d)—(f)两类褶皱与正常区域处LiFeAs的能带结构示意图^[109]

Figure 7. (a) STM topography (top) and height profile (bottom) of the first type of wrinkle; (b) STM torphology (top) and height profile (bottom) of the second type of wrinkle; (c) comparison of dI/dV spectra between the two wrinkles and the normal region; (d)–(f) schematic diagram of tuning of LiFeAs band structures by strain^[109].

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图 8 (a)双轴电荷密度波区域的STM图像; (b)图(a)的傅里叶变换: (c)不同区域的dI/dV谱线的比较; (d)图(a)中沿不同方向箭头的空间分辨dI/dV谱线图; (e) 0.5 T下, 双轴电荷密度波区域的0偏压dI/dV map图像; (f)图(e)中红色箭头方向的空间分辨dI/dV谱线图^[61]

Figure 8. (a) STM topography of large area biaxial charge density wave region; (b) corresponding Fourier transform of panel (a); (c) comparison of dI/dV spectra in different regions; (d) dI/dV intensity spectra along the arrows marked in panel (a); (e) zero bias dI/dV map of the biaxial CDW region under 0.5 T magnetic field; (f) intensity plot of the dI/dV spectra along the red arrow in panel (e)^[61].

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图 9 大面积、有序可调马约拉纳零能模阵列的形成, (上半部分)不同磁场下的马约拉纳零能模阵列, (下半部分) 6 T下微米尺度有序的马约拉纳零能模阵列^[61]

Figure 9. Formation of large-scale, ordered and tunable MZM lattice. Upper panel: Series of zero energy dI/dV maps of the MZM vortices in the biaxial CDW region under magnetic fields of 0.5, 2, 4, 5, and 6 T. Lower panel: Micrometer-sized ordered MZM lattice under 6 T^[61].

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图 10 (a)磁通涡旋的数量和间距随磁场的变化; (b)不同磁场下的平均dI/dV谱线^[61]

Figure 10. (a) Number (black) and the spacing of neighboring vortices (red) under different magnetic fields, the scanning area is 240 nm × 240 nm; (b) averaged dI/dV spectra under different magnetic fields^[61].

DownLoad: Full-Size Img PowerPoint

图 11 基于马约拉纳零能模阵列的可能编织方案, 包括利用STM针尖物理上移动涡旋和只通过测量实现编织的方案

Figure 11. Schematic of possible braiding approaches based on the MZM lattice. Upper panel: Physically move the vortices around each other using a STM tip. Lower panel: Measurement-only approach without physically moving the vortices.

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[1]	Majorana E 1937 Nuovo Ciment 14 171 Google Scholar
[2]	Avignone F T, Elliott S R, Engel J 2008 Rev. Mod. Phys. 80 481 Google Scholar
[3]	Arnquist I J, Avignone III F T, Barabash A S, Barton C J, Barton P J, Bhimani K H, Blalock E, Bos B, Busch M, Buuck M, Caldwell T S, Chan Y D, Christofferson C D, Chu P H, Clark M L, Cuesta C, Detwiler J A, Efremenko Yu, Ejiri H, Elliott S R, Giovanetti G K, Green M P, Gruszko J, Guinn I S, Guiseppe V E, Haufe C 3Lopez A M, López-Castàno J M, Martin E L, Martin R D, Massarczyk R, Meijer S J, Mertens S, Oli T K, Othman G, Paudel L S, Pettus W, Poon A W P, Radford D C, Reine A L, Rielage K, Ruof N W, Schaper D C, Tedeschi D, Varner R L, Vasilyev S, Wilkerson J F, Wiseman C, Xu W, Yu C H, Zhu B X 2023 Phys. Rev. Lett. 130 062501 Google Scholar
[4]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[5]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[6]	Kitaev A Y 2003 Ann. Phys-New. York. 303 2 Google Scholar
[7]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[8]	Aasen D, Hell M, Mishmash R V, Higginbotham A, Danon J, Leijnse M, Jespersen T S, Folk J A, Marcus C M, Flensberg K, Alicea J 2016 Phys. Rev. X 6 031016 Google Scholar
[9]	Moore G, Read N 1991 Nucl. Phys. B 360 362 Google Scholar
[10]	Read N, Green D 2000 Phys. Rev. B 61 10267 Google Scholar
[11]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[12]	Kitaev A Y 2001 Phys. Uspekhi 44 131 Google Scholar
[13]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[14]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[15]	Sau J D, Lutchyn R M, Tewari S, Das Sarma S 2010 Phys. Rev. Lett. 104 040502 Google Scholar
[16]	Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407 Google Scholar
[17]	Braunecker B, Simon P 2013 Phys. Rev. Lett. 111 147202 Google Scholar
[18]	Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805 Google Scholar
[19]	Li J, Neupert T, Wang Z J, MacDonald A H, Yazdani A, Bernevig B A 2016 Nat. Commun. 7 12297 Google Scholar
[20]	Maeno Y, Hashimoto H, Yoshida K, Nishizaki S, Fujita T, Bednorz J G, Lichtenberg F 1994 Nature 372 532 Google Scholar
[21]	Kallin C 2012 Rep. Prog. Phys. 75 042501 Google Scholar
[22]	Hassinger E, Bourgeois-Hope P, Taniguchi H, de Cotret S R, Grissonnanche G, Anwar M S, Maeno Y, Doiron-Leyraud N, Taillefer L 2017 Phys. Rev. X 7 011032 Google Scholar
[23]	Ran S, Eckberg C, Ding Q P, Furukawa Y, Metz T, Saha S R, Liu I L, Zic M, Kim H, Paglione J, Butch N P 2019 Science 365 684 Google Scholar
[24]	Jiao L, Howard S, Ran S, Wang Z Y, Rodriguez J O, Sigrist M, Wang Z Q, Butch N P, Madhavan V 2020 Nature 579 523 Google Scholar
[25]	Pustogow A, Luo Y K, Chronister A, Su Y S, Sokolov D A, Jerzembeck F, Mackenzie A P, Hicks C W, Kikugawa N, Raghu S, Bauer E D, Brown S E 2019 Nature 574 72 Google Scholar
[26]	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
[27]	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
[28]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[29]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[30]	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 Google Scholar
[31]	Ruby M, Pientka F, Peng Y, von Oppen F, Heinrich B W, Franke K J 2015 Phys. Rev. Lett. 115 197204 Google Scholar
[32]	Kim H, Palacio-Morales A, Posske T, Rozsa L, Palotas K, Szunyogh L, Thorwart M, Wiesendanger R 2018 Sci. Adv. 4 eaar5251 Google Scholar
[33]	Palacio-Morales A, Mascot E, Cocklin S, Kim H, Rachel S, Morr D K, Wiesendanger R 2019 Sci. Adv. 5 eaav6600 Google Scholar
[34]	Kezilebieke S, Huda M N, Vano V, Aapro M, Ganguli S C, Silveira O J, Glodzik S, Foster A S, Ojanen T, Liljeroth P 2020 Nature 588 424 Google Scholar
[35]	Kezilebieke S, Silveira O J, Huda M N, Vano V, Aapro M, Ganguli S C, Lahtinen J, Mansell R, van Dijken S, Foster A S, Liljeroth P 2021 Adv. Mater. 33 2006850 Google Scholar
[36]	Zheng H, Jia J F 2019 Chin. Phys. B 28 067403 Google Scholar
[37]	Chen M Y, Chen X Y, Yang H, Du Z Y, Wen H H 2018 Sci. Adv. 4 eaat1084 Google Scholar
[38]	Liang J, Zhang Y J, Yao X, Li H, Li Z X, Wang J N, Chen Y Z, Sou I K 2020 P. Natl. Acad. Sci. Usa. 117 221 Google Scholar
[39]	Jack B, Xie Y L, Yazdani A 2021 Nat. Rev. Phys. 3 541 Google Scholar
[40]	Yuan Y H, Pan J, Wang X T, Fang Y Q, Song C L, Wang L L, He K, Ma X C, Zhang H J, Huang F Q, Li W, Xue Q K 2019 Nat. Phys. 15 1046 Google Scholar
[41]	Nayak A K, Steinbok A, Roet Y, Koo J, Margalit G, Feldman I, Almoalem A, Kanigel A, Fiete G A, Yan B H, Oreg Y, Avraham N, Beidenkopf H 2021 Nat. Phys. 17 1413 Google Scholar
[42]	Lv Y F, Wang W L, Zhang Y M, Ding H, Li W, Wang L L, He K, Song C L, Ma X C, Xue Q K 2017 Sci. Bull. 62 852 Google Scholar
[43]	Wray L A, Xu S Y, Xia Y Q, Hor Y S, Qian D, Fedorov A V, Lin H, Bansil A, Cava R J, Hasan M Z 2010 Nat. Phys. 6 855 Google Scholar
[44]	Tao R, Yan Y J, Liu X, Wang Z W, Ando Y, Wang Q H, Zhang T, Feng D L 2018 Phys. Rev. X 8 041024 Google Scholar
[45]	Tanaka Y, Nakayama K, Souma S, Sato T, Xu N, Zhang P, Richard P, Ding H, Suzuki Y, Das P, Kadowaki K, Takahashi T 2012 Phys. Rev. B 85 125111 Google Scholar
[46]	Khim S, Landaeta J F, Banda J, Bannor N, Brando M, Brydon P M R, Hafner D, Kuchler R, Cardoso-Gil R, Stockert U, Mackenzie A P, Agterberg D F, Geibel C, Hassinger E 2021 Science 373 1012 Google Scholar
[47]	Landaeta J F, Khanenko P, Cavanagh D C, Geibel C, Khim S, Mishra S, Sheikin I, Brydon P M R, Agterberg D F, Brando M, Hassinger E 2022 Phys. Rev. X 12 031001 Google Scholar
[48]	Ortiz B R, Teicher S M L, Hu Y, Zuo J L, Sarte P M, Schueller E C, Abeykoon A M M, Krogstad M J, Rosenkranz S, Osborn R, Seshadri R, Balents L, He J F, Wilson S D 2020 Phys. Rev. Lett. 125 247002 Google Scholar
[49]	Chen H, Yang H T, Hu B, Zhao Z, Yuan J, Xing Y Q, Qian G J, Huang Z H, Li G, Ye Y H, Ma S, Ni S L, Zhang H, Yin Q W, Gong C S, Tu Z J, Lei H C, Tan H X, Zhou S, Shen C M, Dong X L, Yan B H, Wang Z Q, Gao H J 2021 Nature 599 222 Google Scholar
[50]	Liang Z W, Hou X Y, Zhang F, Ma W R, Wu P, Zhang Z Y, Yu F H, Ying J J, Jiang K, Shan L, Wang Z Y, Chen X H 2021 Phys. Rev. X 11 031026 Google Scholar
[51]	Paglione J, Greene R L 2010 Nat. Phys. 6 645 Google Scholar
[52]	Stewart G R 2011 Rev. Mod. Phys. 83 1589 Google Scholar
[53]	Wen H H, Li S L 2011 Annu. Rev. Condens. Matter Phys. 2 121 Google Scholar
[54]	Fernandes R M, Coldea A I, Ding H, Fisher I R, Hirschfeld P J, Kotliar G 2022 Nature 601 35 Google Scholar
[55]	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 362 333 Google Scholar
[56]	Li G, Zhu S Y, Wang D F, Wang Y L, Gao H J 2021 Supercond. Sci. Tech. 34 073001 Google Scholar
[57]	Li G, Zhu S Y, Fan P, Cao L, Gao H J 2022 Chin. Phys. B 31 080301 Google Scholar
[58]	Liu Q, Chen C, Zhang T, Peng R, Yan Y J, Wen C H P, Lou X, Huang Y L, Tian J P, Dong X L, Wang G W, Bao W C, Wang Q H, Yin Z P, Zhao Z X, Feng D L 2018 Phys. Rev. X 8 041056 Google Scholar
[59]	Liu W Y, Cao L, Zhu S Y, Kong L Y, Wang G W, Papaj M, Zhang P, Liu Y B, Chen H, Li G, Yang F Z, Kondo T, Du S X, Cao G H, Shin S, Fu L, Yin Z P, Gao H J, Ding H 2020 Nat. Commun. 11 5688 Google Scholar
[60]	Kong L Y, Cao L, Zhu S Y, Papaj M, Dai G Y, Li G, Fan P, Liu W Y, Yang F Z, Wang X C, Du S X, Jin C Q, Fu L, Gao H J, Ding H 2021 Nat. Commun. 12 4146 Google Scholar
[61]	Li M, Li G, Cao L, Zhou X T, Wang X C, Jin C Q, Chiu C K, Pennycook S J, Wang Z Q, Gao H J 2022 Nature 606 890 Google Scholar
[62]	Hao N N, Hu J P 2014 Phys. Rev. X 4 031053 Google Scholar
[63]	Hao N, Hu J P 2019 Natl. Sci. Rev. 6 213 Google Scholar
[64]	Wang Z J, Zhang P, Xu G, Zeng L K, Miao H, Xu X Y, Qian T, Weng H M, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B 92 115119 Google Scholar
[65]	Fang M H, Pham H M, Qian B, Liu T J, Vehstedt E K, Liu Y, Spinu L, Mao Z Q 2008 Phys. Rev. B 78 224503 Google Scholar
[66]	Chen G F, Chen Z G, Dong J, Hu W Z, Li G, Zhang X D, Zheng P, Luo J L, Wang N L 2009 Phys. Rev. B 79 140509(R Google Scholar
[67]	Pourret A, Malone L, Antunes A B, Yadav C S, Paulose P L, Fauque B, Behnia K 2011 Phys. Rev. B 83 020504(R Google Scholar
[68]	Homes C C, Dai Y M, Wen J S, Xu Z J, Gu G D 2015 Phys. Rev. B 91 144503 Google Scholar
[69]	Xu G, Lian B, Tang P Z, Qi X L, Zhang S C 2016 Phys. Rev. Lett. 117 047001 Google Scholar
[70]	Zhang Z Y 2017 Sci. Bull. 62 671 Google Scholar
[71]	Qin W, Gao J Q, Cui P, Zhang Z Y 2023 Sci. China-Phys. Mech. Astron. 66 267005 Google Scholar
[72]	Yazdani A, von Oppen F, Halperin B I, Yacoby A 2023 Science 380 eade0850 Google Scholar
[73]	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
[74]	Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T, Tamegai T 2019 Nat. Mater. 18 811 Google Scholar
[75]	Chiu C K, Machida T, Huang Y Y, Hanaguri T, Zhang F C 2020 Sci. Adv. 6 eaay0443 Google Scholar
[76]	Lu X F, Wang N Z, Wu H, Wu Y P, Zhao D, Zeng X Z, Luo X G, Wu T, Bao W, Zhang G H, Huang F Q, Huang Q Z, Chen X H 2015 Nat. Mater. 14 325 Google Scholar
[77]	Huang Y L, Feng Z P, Ni S L, Li J, Hu W, Liu S B, Mao Y Y, Zhou H X, Zhou F, Jin K, Wang H B, Yuan J, Dong X L, Zhao Z X 2017 Chin. Phys. Lett. 34 077404 Google Scholar
[78]	Hayashi N, Isoshima T, Ichioka M, Machida K 1998 Phys. Rev. Lett. 80 2921 Google Scholar
[79]	Khaymovich I M, Kopnin N B, Mel'nikov A S, Shereshevskii I A 2009 Phys. Rev. B 79 224506 Google Scholar
[80]	Hu L H, Li C, Xu D H, Zhou Y, Zhang F C 2016 Phys. Rev. B 94 224501 Google Scholar
[81]	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
[82]	Chen C, Liu Q, Zhang T Z, Li D, Shen P P, Dong X L, Zhao Z X, Zhang T, Feng D L 2019 Chin. Phys. Lett. 36 057403 Google Scholar
[83]	Cao L, Song Y, Liu Y B, Zheng Q, Han G Y, Liu W Y, Li M, Chen H, Xing Y Q, Cao G H, Ding H, Lin X, Du S X, Zhang Y Y, Li G, Wang Z Q, Gao H J 2021 Nano Res. 14 3921 Google Scholar
[84]	Iyo A, Kawashima K, Kinjo T, Nishio T, Ishida S, Fujihisa H, Gotoh Y, Kihou K, Eisaki H, Yoshida Y 2016 J. Am. Chem. Soc. 138 3410 Google Scholar
[85]	Kawakami T, Hu X 2015 Phys. Rev. Lett. 115 177001 Google Scholar
[86]	Wang X C, Liu Q Q, Lv Y X, Gao W B, Yang L X, Yu R C, Li F Y, Jin C Q 2008 Solid State Commun. 148 538 Google Scholar
[87]	Yin J X, Zhang S S, Dai G Y, Zhao Y Y, Kreisel A, Macam G, Wu X X, Miao H, Huang Z Q, Martiny J H J, Andersen B M, Shumiya N, Multer D, Litskevich M, Cheng Z J, Yang X, Cochran T A, Chang G Q, Belopolski I, Xing L Y, Wang X C, Gao Y, Chuang F C, Lin H, Wang Z Q, Jin C Q, Bang Y, Hasan M Z 2019 Phys. Rev. Lett. 123 217004 Google Scholar
[88]	Zhang P, Wang Z J, Wu X X, Yaji K, Ishida Y, Kohama Y, Dai G Y, Sun Y, Bareille C, Kuroda K, Kondo T, Okazaki K, Kindo K, Wang X C, Jin C Q, Hu J P, Thomale R, Sumida K, Wu S L, Miyamoto K, Okuda T, Ding H, Gu G D, Tamegai T, Kawakami T, Sato M, Shin S 2019 Nat. Phys. 15 41 Google Scholar
[89]	Hanaguri T, Kitagawa K, Matsubayashi K, Mazaki Y, Uwatoko Y, Takagi H 2012 Phys. Rev. B 85 214505 Google Scholar
[90]	Hu L H, Wu X X, Liu C X, Zhang R X 2022 Phys. Rev. Lett. 129 277001 Google Scholar
[91]	Konig E J, Coleman P 2019 Phys. Rev. Lett. 122 207001 Google Scholar
[92]	Qin S S, Hu L H, Le C C, Zeng J F, Zhang F C, Fang C, Hu J P 2019 Phys. Rev. Lett. 123 027003 Google Scholar
[93]	Chen C, Jiang K, Zhang Y, Liu C F, Liu Y, Wang Z Q, Wang J 2020 Nat. Phys. 16 536 Google Scholar
[94]	Zhang Y, Jiang K, Zhang F C, Wang J, Wang Z Q 2021 Phys. Rev. X 11 011041 Google Scholar
[95]	Yin J X, Wu Z, Wang J H, Ye Z Y, Gong J, Hou X Y, Shan L, Li A, Liang X J, Wu X X, Li J, Ting C S, Wang Z Q, Hu J P, Hor P H, Ding H, Pan S H 2015 Nat. Phys. 11 543 Google Scholar
[96]	Fan P, Yang F Z, Qian G J, Chen H, Zhang Y Y, Li G, Huang Z H, Xing Y Q, Kong L Y, Liu W Y, Jiang K, Shen C M, Du S X, Schneeloch J, Zhong R D, Gu G D, Wang Z Q, Ding H, Gao H J 2021 Nat. Commun. 12 1348 Google Scholar
[97]	Wang Z Y, Rodriguez J O, Jiao L, Howard S, Graham M, Gu G D, Hughes T L, Morr D K, Madhavan V 2020 Science 367 104 Google Scholar
[98]	Hu J P 2013 Phys. Rev. X 3 031004 Google Scholar
[99]	Hao N N, Hu J P 2014 Phys. Rev. B 89 045144 Google Scholar
[100]	Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001 Google Scholar
[101]	Zhu S, Kong L, Cao L, Chen H, Papaj M, Du S, Xing Y, Liu W, Wang D, Shen C, Yang F, Schneeloch J, Zhong R, Gu G, Fu L, Zhang Y Y, Ding H, Gao H J 2020 Science 367 189 Google Scholar
[102]	Ge J F, Bastiaans K M, Chatzopoulos D, Cho D, Tromp W O, Benschop T, Niu J, Gu G, Allan M P 2022 arXiv: 2205.10346 [cond-mat.supr-con
[103]	于渌 1965 物理学报 21 75 Google Scholar Yu L 1965 Acta Phys. Sin. 21 75 Google Scholar
[104]	Shiba H 1968 Prog. Theor. Phys. 40 435 Google Scholar
[105]	Rusinov A I 1969 JETP Lett. 9 1101
[106]	Caroli C, De Gennes P G, Matricon J 1964 Phys. Lett. 9 307 Google Scholar
[107]	Jeon S, Xie Y L, Li J, Wang Z J, Bernevig B A, Yazdani A 2017 Science 358 772 Google Scholar
[108]	Wang D F, Wiebe J, Zhong R D, Gu G D, Wiesendanger R 2021 Phys. Rev. Lett. 126 076802 Google Scholar
[109]	Cao L, Liu W Y, Li G, Dai G Y, Zheng Q, Wang Y X, Jiang K, Zhu S Y, Huang L, Kong L Y, Yang F Z, Wang X C, Zhou W, Lin X, Hu J P, Jin C Q, Ding H, Gao H J 2021 Nat. Commun. 12 6312 Google Scholar
[110]	Yim C M, Trainer C, Aluru R, Chi S, Hardy W N, Liang R X, Bonn D, Wahl P 2018 Nat. Commun. 9 2602 Google Scholar
[111]	Bonderson P, Freedman M, Nayak C 2009 Ann. Phys-new. York. 324 787 Google Scholar
[112]	Wang Y X, Lin M, Hughes T L 2018 Phys. Rev. B 98 165144 Google Scholar
[113]	Wang Q Y, Liu C C, Lu Y M, Zhang F 2018 Phys. Rev. Lett. 121 186801 Google Scholar
[114]	Hsu C H, Stano P, Klinovaja J, Loss D 2018 Phys. Rev. Lett. 121 196801 Google Scholar
[115]	Li C, Luo X J, Chen L, Liu D E, Zhang F C, Liu X 2022 Natl. Sci. Rev. 9 nwac095 Google Scholar

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[14]	Wang Zhi-Cheng, Cao Guang-Han. Self-doped iron-based superconductors with intergrowth structures. Acta Physica Sinica, 2018, 67(20): 207406. doi: 10.7498/aps.67.20181355
[15]	Du Zeng-Yi, Fang De-Long, Wang Zhen-Yu, Du Guan, Yang Xiong, Yang Huan, Gu Gen-Da, Wen Hai-Hu. Investigation of scanning tunneling spectra on iron-based superconductor FeSe0.5Te0.5. Acta Physica Sinica, 2015, 64(9): 097401. doi: 10.7498/aps.64.097401
[16]	Yu Rong. Electron correlations and orbital selectivities in multiorbital models for iron-based superconductors. Acta Physica Sinica, 2015, 64(21): 217102. doi: 10.7498/aps.64.217102
[17]	Li Shi-Chao, Gan Yuan, Wang Jing-Hui, Ran Ke-Jing, Wen Jin-Sheng. Magnetic neutron scattering studies on the Fe-based superconductor system Fe1+yTe1-xSex. Acta Physica Sinica, 2015, 64(9): 097503. doi: 10.7498/aps.64.097503
[18]	Li Zheng, Zhou Rui, Zheng Guo-Qing. Quantum criticalities in carrier-doped iron-based superconductors. Acta Physica Sinica, 2015, 64(21): 217404. doi: 10.7498/aps.64.217404
[19]	Xing Zhong-Wen, Liu Mei, Li Bin. Magnetism and phonon softening of LiFeAs superconductors. Acta Physica Sinica, 2011, 60(7): 077402. doi: 10.7498/aps.60.077402
[20]	Liu Su, Li Bin, Wang Wei, Wang Jun, Liu Mei. Electronic structure and magnetism of SrFeAsF and Co-doped superconductor SrFe0.875Co0.125AsF. Acta Physica Sinica, 2010, 59(6): 4245-4252. doi: 10.7498/aps.59.4245

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Vol. 73, Issue 3 - 2024-02-05

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