Exploring Majorana zero modes in iron-based superconductors

doi:10.1088/1674-1056/ac70c3

Abstract Majorana zero modes (MZMs) are Majorana-fermion-like quasiparticles existing in crystals or hybrid platforms with topologically non-trivial electronic structures. They obey non-Abelian braiding statistics and are considered promising to realize topological quantum computing. Discovery of MZM in the vortices of the iron-based superconductors (IBSs) has recently fueled the Majorana research in a way which not only removes the material barrier requiring construction of complicated hybrid artificial structures, but also enables observation of pure MZMs under higher temperatures. So far, MZMs have been observed in iron-based superconductors including FeTe_0.55Se_0.45, (Li_0.84Fe_0.16)OHFeSe, CaKFe₄As₄, and LiFeAs. In this topical review, we present an overview of the recent STM studies on the MZMs in IBSs. We start with the observation of MZMs in the vortices in FeTe_0.55Se_0.45 and discuss the pros and cons of FeTe_0.55Se_0.45 compared with other platforms. We then review the following up discovery of MZMs in vortices of CaKFe₄As₄, impurity-assisted vortices of LiFeAs, and quantum anomalous vortices in FeTe_0.55Se_0.45, illustrating the pathway of the developments of MZM research in IBSs. Finally, we give perspective on future experimental works in this field.

Keywords: Majorana zero mode iron-based superconductors topological surface states scanning tunneling microscopy

Received: 07 April 2022
Revised: 17 May 2022
Accepted manuscript online: 18 May 2022

PACS:	03.75.Lm	(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
	74.25.-q	(Properties of superconductors)
	74.70.-b	(Superconducting materials other than cuprates)

Fund: The work is supported by the Ministry of Science and Technology of China (Grant No. 2019YFA0308500) and the Chinese Academy of Sciences (Grant Nos. XDB28000000 and YSBR-003).

Corresponding Authors: Hong-Jun Gao
E-mail: hjgao@iphy.ac.cn

Cite this article:

Geng Li(李更), Shiyu Zhu(朱诗雨), Peng Fan(范朋), Lu Cao(曹路), and Hong-Jun Gao(高鸿钧) Exploring Majorana zero modes in iron-based superconductors 2022 Chin. Phys. B 31 080301

[1] Majorana E 1937 Nuovo Ciment 14 171
[2] Alicea J 2012 Rep. Prog. Phys. 75 076501
[3] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[4] Wilczek F 2009 Nat. Phys. 5 614
[5] Kitaev A Y 2003 Ann. Phys-new. York. 303 2
[6] Beenakker C W J 2013 Annu. Rev. Condens. Matter Phys. 4 113
[7] Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[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 and Alicea J 2016 Phys. Rev. X 6 031016
[9] Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
[10] Read N and Green D 2000 Phys. Rev. B 61 10267
[11] Ivanov D A 2001 Phys. Rev. Lett. 86 268
[12] Kitaev A Y 2001 Phys. Uspekhi 44 131
[13] Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Rev. Lett. 105 077001
[14] Sau J D, Lutchyn R M, Tewari S and Das Sarma S 2010 Phys. Rev. Lett. 104 040502
[15] Braunecker B and Simon P 2013 Phys. Rev. Lett. 111 147202
[16] Klinovaja J, Stano P, Yazdani A and Loss D 2013 Phys. Rev. Lett. 111 186805
[17] Nadj-Perge S, Drozdov I K, Bernevig B A and Yazdani A 2013 Phys. Rev. B 88 020407
[18] Vazifeh M M and Franz M 2013 Phys. Rev. Lett. 111 206802
[19] Li J, Neupert T, Wang Z J, MacDonald A H, Yazdani A and Bernevig B A 2016 Nat. Commun. 7 12297
[20] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M and Kouwenhoven L P 2012 Science 336 1003
[21] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P and Xu H Q 2012 Nano Lett. 12 6414
[22] Churchill H O H, Fatemi V, Grove-Rasmussen K, Deng M T, Caroff P, Xu H Q and Marcus C M 2013 Phys. Rev. B 87 241401
[23] Deng M T, Vaitiekenas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygard J, Krogstrup P and Marcus C M 2016 Science 354 1557
[24] Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M and Oreg Y 2018 Nat. Rev. Mater. 3 52
[25] Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A and Yazdani A 2014 Science 346 602
[26] Ruby M, Pientka F, Peng Y, von Oppen F, Heinrich B W and Franke K J 2015 Phys. Rev. Lett. 115 197204
[27] Ruby M, Heinrich B W, Peng Y, von Oppen F and Franke K J 2017 Nano Lett. 17 4473
[28] Kim H, Palacio-Morales A, Posske T, Rozsa L, Palotas K, Szunyogh L, Thorwart M and Wiesendanger R 2018 Sci. Adv. 4 eaar5251
[29] Schneider L, Beck P, Posske T, Crawford D, Mascot E, Rachel S, Wiesendanger R and Wiebe J 2021 Nat. Phys. 17 943
[30] Schneider L, Beck P, Neuhaus-Steinmetz J, Rozsa L, Posske T, Wiebe J and Wiesendanger R 2022 Nat. Nanotechnol. 17 384
[31] Palacio-Morales A, Mascot E, Cocklin S, Kim H, Rachel S, Morr D K and Wiesendanger R 2019 Sci. Adv. 5 eaav6600
[32] Kezilebieke S, Huda M N, Vano V, Aapro M, Ganguli S C, Silveira O J, Glodzik S, Foster A S, Ojanen T and Liljeroth P 2020 Nature 588 424
[33] 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 and Liljeroth P 2021 Adv. Mater. 33 2006850
[34] 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 and Beidenkopf H 2021 Nat. Phys. 17 1413
[35] Kezilebieke S, Vano V, Huda M N, Aapro M, Ganguli S C, Liljeroth P and Lado J L 2022 Nano Lett. 22 328
[36] 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 and Jia J F 2015 Phys. Rev. Lett. 114 017001
[37] 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 and Jia J F 2016 Phys. Rev. Lett. 116 257003
[38] Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G D, Ding H and Shin S 2018 Science 360 182
[39] 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 and Gao H J 2018 Science 362 333
[40] Li G, Zhu S Y, Wang D F, Wang Y L and Gao H J 2021 Supercond. Sci. Tech. 34 073001
[41] Fernandes R M, Coldea A I, Ding H, Fisher I R, Hirschfeld P J and Kotliar G 2022 Nature 601 35
[42] 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 and Feng D L 2018 Phys. Rev. X 8 041056
[43] 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 and Ding H 2020 Nat. Commun. 11 5688
[44] 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 and Ding H 2021 Nat. Commun. 12 4146
[45] 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 and Gao H J 2020 Science 367 189
[46] Wang Z Y, Rodriguez J O, Jiao L, Howard S, Graham M, Gu G D, Hughes T L, Morr D K and Madhavan V 2020 Science 367 104
[47] Chen C, Jiang K, Zhang Y, Liu C F, Liu Y, Wang Z Q and Wang J 2020 Nat. Phys. 16 536
[48] Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T and Tamegai T 2019 Nat. Mater. 18 811
[49] Caroli C, De Gennes P G and Matricon J 1964 Phys. Lett. 9 307
[50] Hess H F, Robinson R B and Waszczak J V 1990 Phys. Rev. Lett. 64 2711
[51] Zhang P, Richard P, Xu N, Xu Y M, Ma J, Qian T, Fedorov A V, Denlinger J D, Gu G D and Ding H 2014 Appl. Phys. Lett. 105 172601
[52] 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 and Shin S 2019 Nat. Phys. 15 41
[53] 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 and Fang Z 2015 Phys. Rev. B 92 115119
[54] Xu G, Lian B, Tang P Z, Qi X L and Zhang S C 2016 Phys. Rev. Lett. 117 047001
[55] Chiu C K, Machida T, Huang Y Y, Hanaguri T and Zhang F C 2020 Sci. Adv. 6 eaay0443
[56] 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 and Ding H 2019 Nat. Phys. 15 1181
[57] Liu C X, Sau J D, Stanescu T D and Das Sarma S 2017 Phys. Rev. B 96 075161
[58] Moore C, Stanescu T D and Tewari S 2018 Phys. Rev. B 97 165302
[59] Moore C, Zeng C C, Stanescu T D and Tewari S 2018 Phys. Rev. B 98 155314
[60] Flensberg K 2010 Phys. Rev. B 82 180516
[61] Setiawan F, Liu C X, Sau J D and Das Sarma S 2017 Phys. Rev. B 96 184520
[62] Law K T, Lee P A and Ng T K 2009 Phys. Rev. Lett. 103 237001
[63] Wimmer M, Akhmerov A R, Dahlhaus J P and Beenakker C W J 2011 New J. Phys. 13 053016
[64] Sau J 2020 Science 367 145
[65] Sau J, Simon S, Vishveshwara S and Williams J R 2020 Nature Reviews Physics 2 667
[66] He X, Li G, Zhang J, Karki A B, Jin R, Sales B C, Sefat A S, McGuire M A, Mandrus D and Plummer E W 2011 Phys. Rev. B 83 220502
[67] Iyo A, Kawashima K, Kinjo T, Nishio T, Ishida S, Fujihisa H, Gotoh Y, Kihou K, Eisaki H and Yoshida Y 2016 J. Am. Chem. Soc. 138 3410
[68] Meier W R, Kong T, Bud'ko S L and Canfield P C 2017 Phys. Rev. Materials 1 013401
[69] Gao M A, Ma F J, Lu Z Y and Xiang T 2010 Phys. Rev. B 81 193409
[70] Wang X C, Zhang S J, Liu Q Q, Deng Z, Lv Y X, Zhu J L, Feng S M and Jin C Q 2011 High Pressure Res. 31 7
[71] Wang X C, Liu Q Q, Lv Y X, Gao W B, Yang L X, Yu R C, Li F Y and Jin C Q 2008 Solid State Commun. 148 538
[72] Hanaguri T, Kitagawa K, Matsubayashi K, Mazaki Y, Uwatoko Y and Takagi H 2012 Phys. Rev. B 85 214505
[73] Chi S, Grothe S, Liang R X, Dosanjh P, Hardy W N, Burke S A, Bonn D A and Pennec Y 2012 Phys. Rev. Lett. 109 087002
[74] Allan M P, Rost A W, Mackenzie A P, Xie Y, Davis J C, Kihou K, Lee C H, Iyo A, Eisaki H and Chuang T M 2012 Science 336 563
[75] 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 and Hasan M Z 2019 Phys. Rev. Lett. 123 217004
[76] Yim C M, Trainer C, Aluru R, Chi S, Hardy W N, Liang R X, Bonn D and Wahl P 2018 Nat. Commun. 9 2602
[77] Wang Y, Hirschfeld P J and Vekhter I 2012 Phys. Rev. B 85 020506
[78] Umezawa K, Li Y, Miao H, Nakayama K, Liu Z H, Richard P, Sato T, He J B, Wang D M, Chen G F, Ding H, Takahashi T and Wang S C 2012 Phys. Rev. Lett. 108 037002
[79] Balatsky A V, Vekhter I and Zhu J X 2006 Rev. Mod. Phys. 78 373
[80] Konig E J and Coleman P 2019 Phys. Rev. Lett. 122 207001
[81] Qin S S, Hu L H, Le C C, Zeng J F, Zhang F C, Fang C and Hu J P 2019 Phys. Rev. Lett. 123 027003
[82] 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 and Pan S H 2015 Nat. Phys. 11 543
[83] Jiang K, Dai X and Wang Z Q 2019 Phys. Rev. X 9 011033
[84] 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 and Gao H J 2021 Nat. Commun. 12 1348
[85] Wang D, Wiebe J, Zhong R, Gu G and Wiesendanger R 2021 Phys. Rev. Lett. 126 076802
[86] 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 and Gao H J 2021 Nat. Commun. 12 6312
[87] Edelberg D, Kumar H, Shenoy V, Ochoa H and Pasupathy A N 2020 Nat. Phys. 16 1097
[88] Mao J H, Milovanovic S P, Andelkovic M, Lai X Y, Cao Y, Watanabe K, Taniguchi T, Covaci L, Peeters F M, Geim A K, Jiang Y H and Andrei E Y 2020 Nature 584 215
[89] Miao H, Wang L M, Richard P, Wu S F, Ma J, Qian T, Xing L Y, Wang X C, Jin C Q, Chou C P, Wang Z, Ku W and Ding H 2014 Phys. Rev. B 89 220503
[90] Sau J D, Clarke D J and Tewari S 2011 Phys. Rev. B 84 094505
[91] van Heck B, Akhmerov A R, Hassler F, Burrello M and Beenakker C W J 2012 New J. Phys. 14 035019
[92] Vijay S and Fu L 2016 Phys. Rev. B 94 235446
[93] Karzig T, Knapp C, Lutchyn R M, Bonderson P, Hastings M B, Nayak C, Alicea J, Flensberg K, Plugge S, Oreg Y, Marcus C M and Freedman M H 2017 Phys. Rev. B 95 235305

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