Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(2): 027301    DOI: 10.1088/1674-1056/ac7208
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Chiral symmetry protected topological nodal superconducting phase and Majorana Fermi arc

Mei-Ling Lu(卢美玲)1, Yao Wang(王瑶)1, He-Zhi Zhang(张鹤之)1, Hao-Lin Chen(陈昊林)1, Tian-Yuan Cui(崔天元)1, and Xi Luo(罗熙)1,2,†
1 College of Science, University of Shanghai for Science and Technology, Shanghai, China;
2 Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai, China
Abstract  With an external in-plane magnetic field, we show the emergence of a topological nodal superconducting phase of the two-dimensional topological surface states. This nodal superconducting phase is protected by the chiral symmetry with a non-zero magnetic field, and there are corresponding Majorana Fermi arcs (also known as flat band Andreev bound states) connecting the two Majorana nodes along the edges, similar to the case of Weyl semimetal. The topological nodal superconductor is an intermediate phase between two different chiral superconductors, and is stable against the effects of substrates. The two-dimensional effective theory of the nodal superconducting phase also captures the low energy behavior of a three-dimensional lattice model which describes the iron-based superconductor with a thin film geometry. The localizations of the Majorana nodes can be manipulated through external in-plane magnetic fields, which may introduce a non-trivial topological Berry phase between them.
Keywords:  superconducting topological surface states      chiral symmetry      topological nodal superconductor      Majorana Fermi arc  
Received:  03 February 2022      Revised:  27 April 2022      Accepted manuscript online:  23 May 2022
PACS:  73.20.At (Surface states, band structure, electron density of states)  
  74.20.-z (Theories and models of superconducting state)  
  03.65.Vf (Phases: geometric; dynamic or topological)  
Fund: We thank Yue Yu and Ziqiang Wang for helpful discussions. Project supported by the National Natural Science Foundation of China (Grant Nos. 11804223 (MLL, YW, HZZ, HLC, TYC, XL), 11474061 (XL), and 12174067 (XL)).
Corresponding Authors:  Xi Luo     E-mail:  xiluo@usst.edu.cn

Cite this article: 

Mei-Ling Lu(卢美玲), Yao Wang(王瑶), He-Zhi Zhang(张鹤之), Hao-Lin Chen(陈昊林), Tian-Yuan Cui(崔天元), and Xi Luo(罗熙) Chiral symmetry protected topological nodal superconducting phase and Majorana Fermi arc 2023 Chin. Phys. B 32 027301

[1] Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98 106803
[2] Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J and Hasan M Z 2008 Nature 452 970
[3] Zhang H J, Liu C X, Qi X L, Deng X Y, Dai X, Zhang S C and Fang Z 2009 Phys. Rev. B 80 085307
[4] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405
[6] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[7] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[8] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
[9] Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
[10] Kitaev A 2009 AIP Conference Proceedings 1134 22
[11] Hatsugai Y 1993 Phys. Rev. Lett. 71 3697
[12] Wan X G, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B 83 205101
[13] Xu S Y, et al. 2015 Science 349 613
[14] Weng H M, Fang C, Fang Z, Bernevig B A and Dai X 2015 Phys. Rev. X 5 011029
[15] Burkov A A and Balents L 2011 Phys. Rev. Lett. 107 127205
[16] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B, Alidoust N, Bian G, Neupane M, Zhang C, Jia S, Bansil A, Lin H and Hasan M Z 2015 Nat. Commun. 6 7373
[17] Yu R, Weng H M, Fang Z, Dai X and Hu X 2015 Phys. Rev. Lett. 115 036807
[18] Zhao Y X and Wang Z D 2013 Phys. Rev. Lett. 110 240404
[19] Zhang T T, Jiang Y, Song Z D, Huang H, He Y Q, Fang Z, Weng H M and Fang C 2019 Nature 566 475
[20] Vergniory M G, Elcoro L, Felser C, Regnault N, Bernevig B A and Wang Z J 2019 Nature 566 480
[21] Tang F, Po H C, Vishwanath A and Wan X G 2019 Nature 566 486
[22] Li F Y, Li Y D, Kim Y B, Balents L, Yu Y and Chen G 2016 Nat. Commun. 7 12691
[23] Prodan E and Prodan C 2009 Phys. Rev. Lett. 103 248101
[24] Zhang L F, Ren J, Wang J S and Li B W 2010 Phys. Rev. Lett. 105 225901
[25] He H, Qiu C, Ye L, Cai X, Fan X, Ke M, Zhang F and Liu Z 2018 Nature 560 61
[26] Khanikaev A B, Hossein Mousavi S, Tse W K, Kargarian M, MacDonald A H and Shvets G 2013 Nat. Mater. 12 233
[27] Chen W J, Jiang S J, Chen X D, Zhu B C, Zhou L, Dong J W and Chan C T 2014 Nat. Commun. 5 5782
[28] Ding K, Ma G C, Xiao M, Zhang Z Q and Chan C T 2016 Phys. Rev. X 6 021007
[29] Yao S Y and Wang Z 2018 Phys. Rev. Lett. 121 086803
[30] Kitaev A 2003 Ann. Phys. 303 2
[31] Kitaev A 2001 Phys. Usp. 44 131
[32] Lian B, Sun X Q, Vaezi A, Qi X L and Zhang S C 2018 Proc. Natl. Acad. Sci. UA 115 10938
[33] Zhan Y M, Chen Y G, Chen B, Ziqiang Wang, Yu Y and X. Luo 2022 New J. Phys. 24 043009
[34] Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
[35] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003
[36] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P and Xu H Q 2012 Nano Lett. 12 6414
[37] Das A, Ronen Y, Most Y, Oreg Y, Heiblum M and Shtrikman H 2012 Nat. Phys. 8 887
[38] 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
[39] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P and Xu H Q 2014 Sci. Rep. 4 7261
[40] 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
[41] 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
[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 and Xue Q K 2017 Sci. Bull. 62 852
[43] Zhang H et al. 2018 Nature 556 74
[44] Zhang H et al. 2021 arXiv: 2101.11456
[45] 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
[46] Chen C, Jiang K, Zhang Y, Liu C F, Liu Y, Wang Z Q and Wang J 2020 Nat. Phys. 16 536
[47] Chen C, Liu Q, Zhang T Z, Li D, Shen P P, Dong X L, Zhao Z X, Zhang T and Feng D L 2019 Chin. Phys. Lett. 36 057403
[48] Zhang P, et al. 2019 Nat. Phys. 15 41
[49] Liu W, Cao L, Zhu S, Kong L, Wang G, Papaj M, Zhang P, Liu Y B, Chen H, Li G, Yang F, Kondo T, Du S, Cao G H, Shin S, Fu L, Yin Z, Gao H J and Ding H 2020 Nat. Commun. 11 5688
[50] 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
[51] Audouard A, Duc F, Drigo L, Toulemonde P, Karlsson S, Strobel P and Sulpice A 2015 Europhys. Lett. 109 27003
[52] Salamon M B, Cornell N, Jaime M, Balakirev F F, Zakhidov A, Huang J J and Wang H Y 2016 Sci. Rep. 6 21469
[53] Xu G, Lian B, Tang P Z, Qi X L and Zhang S C 2016 Phys. Rev. Lett. 117 047001
[54] Zhang R X and Das Sarma S 2021 Phys. Rev. Lett. 126 137001
[55] Sato M, Tanaka Y, Yada K and Yokoyama T 2011 Phys. Rev. B 83 224511
[56] Nagato Y and Nagai K 1995 Phys. Rev. B 51 16254
[57] Tanaka Y and Kashiwaya S 1996 Phys. Rev. B 53 9371
[58] Tanuma Y, Tanaka Y, Ogata M and Kashiwaya S 1999 Phys. Rev. B 60 9817
[59] Wong C L M, Liu J, Law K T and Lee P A 2013 Phys. Rev. B 88 060504
[60] Sedlmayr N, Aguiar-Hualde J M and Bena C 2015 Phys. Rev. B 91 115415
[61] Schnyder A P and Ryu S 2011 Phys. Rev. B 84 060504
[62] Yang S A, Pan H and Zhang F 2014 Phys. Rev. Lett. 113 046401
[63] Bouhon A, Wu Q S, Slager R, Weng H M, Yazyev O V and Bzdusek T 2020 Nat. Phys. 16 1137
[64] Nakosai S, Tanaka Y and Nagaosa N 2012 Phys. Rev. Lett. 108 147003
[65] Zhang F, Kane C L and Mele E J 2013 Phys. Rev. Lett. 111 056403
[66] Ueno Y, Yamakage A, Tanaka Y and Sato M 2013 Phys. Rev. Lett. 111 087002
[67] Luo X, Chen Y G, Wang Z Q and Yu Y 2020 arXiv: 2003.11752
[68] Zhang Y, Jiang K, Zhang F C, Wang J and Wang Z Q 2021 Phys. Rev. X 11 011041
[69] Fu L and Berg E 2010 Phys. Rev. Lett. 105 097001
[70] Sasaki S, Kriener M, Segawa K, Yada K, Tanaka Y, Sato M and Ando Y 2011 Phys. Rev. Lett. 107 217001
[71] Qin D Y, Iida K, Hatano T, Saito H, Ma Y M, Wang C, Hata S, Naito M and Yamamoto A 2021 Phys. Rev. Mater. 5 014801
[72] McLaughlin N J, Wang H, Huang M, Lee-Wong E, Hu L, Lu H, Yan G Q, Gu G, Wu C, You Y Z and Du C R 2021 Nano Lett. 21 7277
[73] Xu Y M, Huang Y B, Cui X Y, Razzoli E, Radovic M, Shi M, Chen G F, Zheng P, Wang N L, Zhang C L, Dai P C, Hu J P, Wang Z and Ding H 2011 Nat. Phys. 7 198
[1] Local evolutions of nodal points in two-dimensional systems with chiral symmetry
Peiyuan Fu(符培源), Zhesen Yang(杨哲森), Jiangping Hu(胡江平). Chin. Phys. B, 2019, 28(7): 077101.
[2] Transport properties of a ladder with two random dimer chains
Hu Dong-Sheng(胡冬生),Zhu Chen-Ping(朱陈平),and Zhang Yong-Mei(张永梅) . Chin. Phys. B, 2011, 20(1): 017104.
No Suggested Reading articles found!