Non-Abelian topological orders and Majorana fermions in spin-singlet superconductors

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 13, 2010, Pages

  Sato, Masatoshi ^a   Takahashi, Yoshiro ^b   Fujimoto, Satoshi ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78049445626     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.134521     Document Type: Article

References (67)

1. X. G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990). 10.1103/PhysRevB.41. 9377
2. X. G. Wen, Phys. Rev. Lett. 64, 2206 (1990). 10.1103/PhysRevLett.64.2206
3. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 10.1016/0550- 3213(91)90407-O
4. C. Nayak and F. Wilczek, Nucl. Phys. B 479, 529 (1996). 10.1016/0550-3213(96)00430-0
5. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000). 10.1103/PhysRevB.61. 10267
6. D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001). 10.1103/PhysRevLett.86.268
7. M. Stone and S.-B. Chung, Phys. Rev. B 73, 014505 (2006). 10.1103/PhysRevB.73.014505
8. A. Stern, F. von Oppen, and E. Mariani, Phys. Rev. B 70, 205338 (2004). 10.1103/PhysRevB.70.205338
9. M. Stone and R. Roy, Phys. Rev. B 69, 184511 (2004). 10.1103/PhysRevB.69. 184511
10. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008). 10.1103/PhysRevB.78.195125
11. G. E. Volovik, Phys. Rep. 351, 195 (2001). 10.1016/S0370-1573(00)00139-3
12. M. Freedman, A. Kitaev, M. Larsen, and Z. Wang, Bull. Am. Math. Soc. 40, 31 (2003). 10.1090/S0273-0979-02-00964-3
13. A. Kitaev, Ann. Phys. 303, 2 (2003). 10.1016/S0003-4916(02)00018-0
14. S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005). 10.1103/PhysRevLett.94.166802
15. N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). 10.1103/PhysRevB.59. 8084
16. N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991). 10.1103/PhysRevB.44.9667
17. S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, Phys. Rev. Lett. 98, 010506 (2007). 10.1103/PhysRevLett.98.010506
18. C. Zhang, S. Tewari, R. M. Lutchyn, and S. Das Sarma, Phys. Rev. Lett. 101, 160401 (2008). 10.1103/PhysRevLett.101.160401
19. Y. Tsutsumi, T. Kawakami, T. Mizushima, M. Ichioka, and K. Machida, Phys. Rev. Lett. 101, 135302 (2008). 10.1103/PhysRevLett.101.135302
20. N. R. Cooper and G. V. Shlyapnikov, Phys. Rev. Lett. 103, 155302 (2009). 10.1103/PhysRevLett.103.155302
21. M. Sato and S. Fujimoto, Phys. Rev. B 79, 094504 (2009). 10.1103/PhysRevB.79.094504
22. M. Sato, Phys. Rev. B 81, 220504 (R) (2010). 10.1103/PhysRevB.81.220504
23. L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008). 10.1103/PhysRevLett.100.096407
24. M. Sato, Phys. Lett. B 575, 126 (2003). 10.1016/j.physletb.2003.09.047
25. In contrast to other non-Abelian topological phases, the systems considered in Refs. do not break the time-reversal invariance in the ground state. Thus the Chern number is trivially zero. Nevertheless, the index theorem ensures the existence of a topologically stable Majorana zero mode in a vortex, which implies that the vortices obey the non-Abelian statistics. See Appendix.
26. M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009); 10.1103/PhysRevLett.103.020401
27. M. Sato, Y. Takahashi, and S. Fujimoto, e-print arXiv:0901.4693v1 (unpublished).
28. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010). 10.1103/PhysRevLett.104.040502
29. J. Alicea, Phys. Rev. B 81, 125318 (2010). 10.1103/PhysRevB.81.125318
30. M. Cheng, R. M. Lutchyn, V. Galitski, and S. Das Sarma, Phys. Rev. Lett. 103, 107001 (2009). 10.1103/PhysRevLett.103.107001
31. E. I. Rashba, Sov. Phys. Solid State 2, 1109 (1960).
32. V. M. Edelstein, Sov. Phys. JETP 68, 1244 (1989).
33. L. P. Gor'kov and E. I. Rashba, Phys. Rev. Lett. 87, 037004 (2001). 10.1103/PhysRevLett.87.037004
34. P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist, Phys. Rev. Lett. 92, 097001 (2004). 10.1103/PhysRevLett.92.097001
35. S. Fujimoto, J. Phys. Soc. Jpn. 76, 034712 (2007). 10.1143/JPSJ.76.034712
36. S. Fujimoto, J. Phys. Soc. Jpn. 76, 051008 (2007). 10.1143/JPSJ.76.051008
37. M. Sato, Phys. Rev. B 73, 214502 (2006). 10.1103/PhysRevB.73.214502
38. The argument here was first outlined in the preprint version of Ref..
39. Note that the definition of the Chern number in Ref. is different from the TKNN number in this paper by a factor - 1.
40. C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964). 10.1016/0031-9163(64)90375-0
41. J. Sau, R. Lutchyn, S. Tewari, and S. Das Sarma, arXiv:0912.4508 (unpublished).
42. A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Phys. Rev. Lett. 102, 216404 (2009). 10.1103/PhysRevLett.102.216404
43. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. B 22, 2099 (1980). 10.1103/PhysRevB.22.2099
44. R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976). 10.1103/PhysRevD.13.3398
45. K. Izawa, Y. Kasahara, Y. Matsuda, K. Behnia, T. Yasuda, R. Settai, and Y. Onuki, Phys. Rev. Lett. 94, 197002 (2005). 10.1103/PhysRevLett.94.197002
46. I. Bonalde, W. Bramer-Escamilla, and E. Bauer, Phys. Rev. Lett. 94, 207002 (2005). 10.1103/PhysRevLett.94.207002
47. N. Kimura, K. Ito, K. Saitoh, Y. Umeda, H. Aoki, and T. Terashima, Phys. Rev. Lett. 95, 247004 (2005). 10.1103/PhysRevLett.95.247004
48. I. Sugitani, J. Phys. Soc. Jpn. 75, 043703 (2006). 10.1143/JPSJ.75.043703
49. H. Mukuda, T. Fujii, T. Ohara, A. Harada, M. Yashima, Y. Kitaoka, Y. Okuda, R. Settai, and Y. Onuki, Phys. Rev. Lett. 100, 107003 (2008). 10.1103/PhysRevLett.100.107003
50. Y. Tada, N. Kawakami, and S. Fujimoto, Phys. Rev. Lett. 101, 267006 (2008). 10.1103/PhysRevLett.101.267006
51. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett. 93, 050401 (2004). 10.1103/PhysRevLett.93.050401
52. J. K. Chin, D. E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, and W. Ketterle, Nature (London) 443, 961 (2006). 10.1038/nature05224
53. K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 95, 010403 (2005). 10.1103/PhysRevLett.95.010403
54. J. Ruseckas, G. Juzeliunas, P. Ohberg, and M. Fleischhauer, Phys. Rev. Lett. 95, 010404 (2005). 10.1103/PhysRevLett.95.010404
55. S. L. Zhu, H. Fu, C. J. Wu, S. C. Zhang, and L. M. Duan, Phys. Rev. Lett. 97, 240401 (2006). 10.1103/PhysRevLett.97.240401
56. T. D. Stanescu, C. Zhang, and V. Galitski, Phys. Rev. Lett. 99, 110403 (2007). 10.1103/PhysRevLett.99.110403
57. D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003). 10.1088/1367-2630/5/ 1/356
58. E. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek, Nucl. Phys. B 516, 704 (1998). 10.1016/S0550-3213(98)00111-4
59. W. J. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, Opt. Express 11, 2053 (2003). 10.1364/OE.11.002053
60. B. Kumar and B. S. Shastry, Phys. Rev. B 68, 104508 (2003). 10.1103/PhysRevB.68.104508
61. Q. H. Wang, D. H. Lee, and P. A. Lee, Phys. Rev. B 69, 092504 (2004). 10.1103/PhysRevB.69.092504
62. M. Sato, Phys. Rev. B 79, 214526 (2009). 10.1103/PhysRevB.79.214526
63. X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 78, 195424 (2008). 10.1103/PhysRevB.78.195424
64. S. Fujimoto, Phys. Rev. B 77, 220501 (R) (2008). 10.1103/PhysRevB.77. 220501
65. R. Jackiw and P. Rossi, Nucl. Phys. B 190, 681 (1981). 10.1016/0550-3213(81)90044-4
66. C. G. Callan, Jr. and J. A. Harvey, Nucl. Phys. B 250, 427 (1985). 10.1016/0550-3213(85)90489-4
67. G. W. Semenoff, Phys. Rev. D 37, 2838 (1988). 10.1103/PhysRevD.37.2838