基于Yu-Shiba-Rusinov态的拓扑超导理论

李牮

doi:10.7498/aps.69.20200831

摘要

Yu-Shiba-Rusinov态是由磁性杂质原子在超导体中诱导出的超导能隙内的束缚态. 它们可以作为构造拓扑超导态的基本单元. 本文阐述了基于Yu-Shiba-Rusinov态的不同维度拓扑超导的统一理论框架, 并通过简单的特例加以解释. 这里的理论是理解多个相关实验的基础.

关键词:

Yu-Shiba-Rusinov states are subgap bound states induced by magnetic impurity atoms in a superconductor. These states can be used as building blocks in constructing an effective topological superconductor. Here we formulate a unified theory of topological superconductivity in different dimensions based on Yu-Shiba-Rusinov states, and demonstrate its application with simple but illustrative examples. Such a theory underlies a number of recent experiments on the related platform.

Keywords:

作者及机构信息

李牮^1,2

1.
西湖大学理学院, 杭州　310024

2.
浙江西湖高等研究院理学研究所, 杭州　310024

通信作者: 李牮, lijian@westlake.edu.cn

基金项目: 国家自然科学基金(批准号: 11774317)支持的课题

Authors and contacts

Li Jian^1,2

1.
School of Science, Westlake University, Hangzhou 310024, China

2.
Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, China

Corresponding author: Li Jian, lijian@westlake.edu.cn

Funds: Project supported by the National Natural Foundation of China (Grant No. 11774317)

文章全文 : translate this paragraph

参考文献

[1]	Kitaev A Y 2001 Physics-Uspekhi 44 131 Google Scholar
[2]	Read N, Green D 2000 Phys. Rev. B 61 10267.
[3]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[4]	Kitaev A 2009 AIP Conference Proceedings 1134 22
[5]	Schnyder A P, Ryu S, Furusaki A, Ludwig A W W 2009 AIP Conference Proceedings 1134 10
[6]	Ryu S, Schnyder A P, Furusaki A, Ludwig A W W 2010 New J. Phys. 12 065010 Google Scholar
[7]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[8]	Beenakker C 2013 Ann. Rev. Condens. Matter Phys. 4 113 Google Scholar
[9]	Chiu C K, Teo J C, Schnyder A P, Ryu S 2016 Rev. Mod. Phys. 88 035005 Google Scholar
[10]	Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M, Oreg Y 2017 arXiv: 1707.04899
[11]	Kitaev A Y 2003 Ann. Phys. 303 2 Google Scholar
[12]	Nayak C, Simon S, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[13]	于渌 1965 物理学报 21 75 Google Scholar Yu L 1965 Acta Phys. Sin. 21 75 Google Scholar
[14]	Shiba H 1968 Pro. Theo. Phys. 40 435 Google Scholar
[15]	Rusinov A I 1969 Soviet Phys. JETP 29 1101
[16]	Choy T P, Edge J M, Akhmerov A R, Beenakker C W J 2011 Physi. Rev. B 84 195442 Google Scholar
[17]	Martin I, Morpurgo A F 2012 Phys. Rev. B 85 144505 Google Scholar
[18]	Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407 Google Scholar
[19]	Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805 Google Scholar
[20]	Braunecker B, Simon P 2013 Phys. Rev. Lett. 111 147202 Google Scholar
[21]	Vazifeh M M, Franz M 2013 Phys. Rev. Lett. 111 206802 Google Scholar
[22]	Pientka F, Glazman L I, von Oppen F 2013 Phys. Rev. B 88 155420 Google Scholar
[23]	Nadj-Perge S, Drozdov I K, Li J, et al. 2014 Science 346 602 Google Scholar
[24]	Li J, Chen H, Drozdov I K, Yazdani A, Bernevig B A, MacDonald A H 2014 Phys. Rev. B 90 235433 Google Scholar
[25]	Röntynen J, Ojanen T 2015 Phys. Rev. Lett. 114 236803 Google Scholar
[26]	Westström A, Pöyhönen K, Ojanen T 2015 Phys. Rev. B 91 064502 Google Scholar
[27]	Li J, Neupert T, Bernevig B A, Yazdani A 2016 Nat. Commun. 7 10395 Google Scholar
[28]	Li J, Neupert T, Wang Z, MacDonald A H, Yazdani A, Bernevig B A 2016 Nat. Commun. 7 12297 Google Scholar
[29]	Feldman B E, Randeria M T, Li J, et al. 2017 Nat. Phys. 13 286 Google Scholar
[30]	Jeon S, Xie Y, Li J, Wang Z, Bernevig B A, Yazdani A 2017 Science 358 772
[31]	Li J, Jeon S, Xie Y, Yazdani A, Bernevig B A 2018 Phys. Rev. B 97 125119 Google Scholar
[32]	Pöyhönen K, Sahlberg I, Westström A, Ojanen T 2018 Nat. Commun. 9 2103
[33]	Kim H, Palacio-Morales A, Posske T, et al. 2018 Science Advances 4 eaar5251 Google Scholar
[34]	Palacio-Morales A, Mascot E, Cocklin S, et al. 2019 Science Advances 5 eaav6600
[35]	Yazdani A, Jones B A, Lutz C P, Crommie M F, Eigler D M 1997 Science 275 1767 Google Scholar
[36]	Sarma S D, Freedman M, Nayak C 2015 npj Quantum Information 1 15001 Google Scholar
[37]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[38]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[39]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[40]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[41]	Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887 Google Scholar
[42]	Rokhinson L P, Liu X, Furdyna J K 2012 Nat. Phys. 8 795 Google Scholar
[43]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[44]	Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003 Google Scholar
[45]	Hu L H, Li C, Xu D H, Zhou Y, Zhang F C 2016 Phys. Rev. B 94 224501 Google Scholar
[46]	Wang D, Kong L, Fan P, et al. 2018 Science 362 333 Google Scholar
[47]	Liu Q, Chen C, Zhang T, et al. 2018 Phys. Rev. X 8 041056
[48]	Jäck B, Xie Y, Li J, Jeon S, Bernevig B A, Yazdani A 2019 Science 364 1255 Google Scholar
[49]	Peng Y, Pientka F, Glazman L I, von Oppen F 2015 Phys. Rev. Lett. 114 106801 Google Scholar
[50]	Duan W, Li J unpublished
[51]	Altland A, Zirnbauer M R 1997 Phys. Rev. B 55 1142
[52]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405
[53]	Wilczek F 2009 Nat. Phys. 5 614 Google Scholar
[54]	Elliott S R, Franz M 2015 Rev. Mod. Phys. 87 137 Google Scholar
[55]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[56]	Fidkowski L, Kitaev A 2010 Phys. Rev. B 81 134509 Google Scholar
[57]	Fidkowski L, Kitaev A 2011 Phys. Rev. B 83 075103 Google Scholar

施引文献

[1]	Kitaev A Y 2001 Physics-Uspekhi 44 131 Google Scholar
[2]	Read N, Green D 2000 Phys. Rev. B 61 10267.
[3]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[4]	Kitaev A 2009 AIP Conference Proceedings 1134 22
[5]	Schnyder A P, Ryu S, Furusaki A, Ludwig A W W 2009 AIP Conference Proceedings 1134 10
[6]	Ryu S, Schnyder A P, Furusaki A, Ludwig A W W 2010 New J. Phys. 12 065010 Google Scholar
[7]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[8]	Beenakker C 2013 Ann. Rev. Condens. Matter Phys. 4 113 Google Scholar
[9]	Chiu C K, Teo J C, Schnyder A P, Ryu S 2016 Rev. Mod. Phys. 88 035005 Google Scholar
[10]	Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M, Oreg Y 2017 arXiv: 1707.04899
[11]	Kitaev A Y 2003 Ann. Phys. 303 2 Google Scholar
[12]	Nayak C, Simon S, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[13]	于渌 1965 物理学报 21 75 Google Scholar Yu L 1965 Acta Phys. Sin. 21 75 Google Scholar
[14]	Shiba H 1968 Pro. Theo. Phys. 40 435 Google Scholar
[15]	Rusinov A I 1969 Soviet Phys. JETP 29 1101
[16]	Choy T P, Edge J M, Akhmerov A R, Beenakker C W J 2011 Physi. Rev. B 84 195442 Google Scholar
[17]	Martin I, Morpurgo A F 2012 Phys. Rev. B 85 144505 Google Scholar
[18]	Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407 Google Scholar
[19]	Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805 Google Scholar
[20]	Braunecker B, Simon P 2013 Phys. Rev. Lett. 111 147202 Google Scholar
[21]	Vazifeh M M, Franz M 2013 Phys. Rev. Lett. 111 206802 Google Scholar
[22]	Pientka F, Glazman L I, von Oppen F 2013 Phys. Rev. B 88 155420 Google Scholar
[23]	Nadj-Perge S, Drozdov I K, Li J, et al. 2014 Science 346 602 Google Scholar
[24]	Li J, Chen H, Drozdov I K, Yazdani A, Bernevig B A, MacDonald A H 2014 Phys. Rev. B 90 235433 Google Scholar
[25]	Röntynen J, Ojanen T 2015 Phys. Rev. Lett. 114 236803 Google Scholar
[26]	Westström A, Pöyhönen K, Ojanen T 2015 Phys. Rev. B 91 064502 Google Scholar
[27]	Li J, Neupert T, Bernevig B A, Yazdani A 2016 Nat. Commun. 7 10395 Google Scholar
[28]	Li J, Neupert T, Wang Z, MacDonald A H, Yazdani A, Bernevig B A 2016 Nat. Commun. 7 12297 Google Scholar
[29]	Feldman B E, Randeria M T, Li J, et al. 2017 Nat. Phys. 13 286 Google Scholar
[30]	Jeon S, Xie Y, Li J, Wang Z, Bernevig B A, Yazdani A 2017 Science 358 772
[31]	Li J, Jeon S, Xie Y, Yazdani A, Bernevig B A 2018 Phys. Rev. B 97 125119 Google Scholar
[32]	Pöyhönen K, Sahlberg I, Westström A, Ojanen T 2018 Nat. Commun. 9 2103
[33]	Kim H, Palacio-Morales A, Posske T, et al. 2018 Science Advances 4 eaar5251 Google Scholar
[34]	Palacio-Morales A, Mascot E, Cocklin S, et al. 2019 Science Advances 5 eaav6600
[35]	Yazdani A, Jones B A, Lutz C P, Crommie M F, Eigler D M 1997 Science 275 1767 Google Scholar
[36]	Sarma S D, Freedman M, Nayak C 2015 npj Quantum Information 1 15001 Google Scholar
[37]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[38]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[39]	Alicea J 2012 Rep. Prog. Phys. 75 076501 Google Scholar
[40]	Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 Google Scholar
[41]	Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887 Google Scholar
[42]	Rokhinson L P, Liu X, Furdyna J K 2012 Nat. Phys. 8 795 Google Scholar
[43]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[44]	Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003 Google Scholar
[45]	Hu L H, Li C, Xu D H, Zhou Y, Zhang F C 2016 Phys. Rev. B 94 224501 Google Scholar
[46]	Wang D, Kong L, Fan P, et al. 2018 Science 362 333 Google Scholar
[47]	Liu Q, Chen C, Zhang T, et al. 2018 Phys. Rev. X 8 041056
[48]	Jäck B, Xie Y, Li J, Jeon S, Bernevig B A, Yazdani A 2019 Science 364 1255 Google Scholar
[49]	Peng Y, Pientka F, Glazman L I, von Oppen F 2015 Phys. Rev. Lett. 114 106801 Google Scholar
[50]	Duan W, Li J unpublished
[51]	Altland A, Zirnbauer M R 1997 Phys. Rev. B 55 1142
[52]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405
[53]	Wilczek F 2009 Nat. Phys. 5 614 Google Scholar
[54]	Elliott S R, Franz M 2015 Rev. Mod. Phys. 87 137 Google Scholar
[55]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[56]	Fidkowski L, Kitaev A 2010 Phys. Rev. B 81 134509 Google Scholar
[57]	Fidkowski L, Kitaev A 2011 Phys. Rev. B 83 075103 Google Scholar

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