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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.
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关键词:
- 拓扑相 /
- 拓扑超导体 /
- 马约拉纳费米子 /
- 磁性杂质 /
- Yu-Shiba-Rusinov态
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:
- topological phase /
- topological superconductivity /
- Majorana fermion /
- magnetic impurity /
- Yu-Shiba-Rusinov state
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[15] Rusinov A I 1969 Soviet Phys. JETP 29 1101
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[26] Westström A, Pöyhönen K, Ojanen T 2015 Phys. Rev. B 91 064502Google Scholar
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[35] Yazdani A, Jones B A, Lutz C P, Crommie M F, Eigler D M 1997 Science 275 1767Google Scholar
[36] Sarma S D, Freedman M, Nayak C 2015 npj Quantum Information 1 15001Google Scholar
[37] Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001Google Scholar
[38] Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002Google Scholar
[39] Alicea J 2012 Rep. Prog. Phys. 75 076501Google Scholar
[40] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003Google Scholar
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[42] Rokhinson L P, Liu X, Furdyna J K 2012 Nat. Phys. 8 795Google Scholar
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[44] Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003Google Scholar
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[48] Jäck B, Xie Y, Li J, Jeon S, Bernevig B A, Yazdani A 2019 Science 364 1255Google Scholar
[49] Peng Y, Pientka F, Glazman L I, von Oppen F 2015 Phys. Rev. Lett. 114 106801Google 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[50] Duan W, Li J unpublished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 614Google Scholar
[54] Elliott S R, Franz M 2015 Rev. Mod. Phys. 87 137Google Scholar
[55] Ivanov D A 2001 Phys. Rev. Lett. 86 268Google Scholar
[56] Fidkowski L, Kitaev A 2010 Phys. Rev. B 81 134509Google Scholar
[57] Fidkowski L, Kitaev A 2011 Phys. Rev. B 83 075103Google Scholar
-
[1] Kitaev A Y 2001 Physics-Uspekhi 44 131Google Scholar
[2] Read N, Green D 2000 Phys. Rev. B 61 10267.
[3] Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407Google 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 065010Google Scholar
[7] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar
[8] Beenakker C 2013 Ann. Rev. Condens. Matter Phys. 4 113Google Scholar
[9] Chiu C K, Teo J C, Schnyder A P, Ryu S 2016 Rev. Mod. Phys. 88 035005Google 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 2Google Scholar
[12] Nayak C, Simon S, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083Google Scholar
[13] 于渌 1965 物理学报 21 75Google Scholar
Yu L 1965 Acta Phys. Sin. 21 75Google Scholar
[14] Shiba H 1968 Pro. Theo. Phys. 40 435Google 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 195442Google Scholar
[17] Martin I, Morpurgo A F 2012 Phys. Rev. B 85 144505Google Scholar
[18] Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407Google Scholar
[19] Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805Google Scholar
[20] Braunecker B, Simon P 2013 Phys. Rev. Lett. 111 147202Google Scholar
[21] Vazifeh M M, Franz M 2013 Phys. Rev. Lett. 111 206802Google Scholar
[22] Pientka F, Glazman L I, von Oppen F 2013 Phys. Rev. B 88 155420Google Scholar
[23] Nadj-Perge S, Drozdov I K, Li J, et al. 2014 Science 346 602Google Scholar
[24] Li J, Chen H, Drozdov I K, Yazdani A, Bernevig B A, MacDonald A H 2014 Phys. Rev. B 90 235433Google Scholar
[25] Röntynen J, Ojanen T 2015 Phys. Rev. Lett. 114 236803Google Scholar
[26] Westström A, Pöyhönen K, Ojanen T 2015 Phys. Rev. B 91 064502Google Scholar
[27] Li J, Neupert T, Bernevig B A, Yazdani A 2016 Nat. Commun. 7 10395Google Scholar
[28] Li J, Neupert T, Wang Z, MacDonald A H, Yazdani A, Bernevig B A 2016 Nat. Commun. 7 12297Google Scholar
[29] Feldman B E, Randeria M T, Li J, et al. 2017 Nat. Phys. 13 286Google 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 125119Google 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 eaar5251Google 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 1767Google Scholar
[36] Sarma S D, Freedman M, Nayak C 2015 npj Quantum Information 1 15001Google Scholar
[37] Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001Google Scholar
[38] Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002Google Scholar
[39] Alicea J 2012 Rep. Prog. Phys. 75 076501Google Scholar
[40] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003Google Scholar
[41] Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887Google Scholar
[42] Rokhinson L P, Liu X, Furdyna J K 2012 Nat. Phys. 8 795Google Scholar
[43] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414Google Scholar
[44] Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003Google Scholar
[45] Hu L H, Li C, Xu D H, Zhou Y, Zhang F C 2016 Phys. Rev. B 94 224501Google Scholar
[46] Wang D, Kong L, Fan P, et al. 2018 Science 362 333Google 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 1255Google Scholar
[49] Peng Y, Pientka F, Glazman L I, von Oppen F 2015 Phys. Rev. Lett. 114 106801Google 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 614Google Scholar
[54] Elliott S R, Franz M 2015 Rev. Mod. Phys. 87 137Google Scholar
[55] Ivanov D A 2001 Phys. Rev. Lett. 86 268Google Scholar
[56] Fidkowski L, Kitaev A 2010 Phys. Rev. B 81 134509Google Scholar
[57] Fidkowski L, Kitaev A 2011 Phys. Rev. B 83 075103Google Scholar
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