Classification of topological insulators and superconductors

AIP Conference Proceedings

Volumn 1134, Issue , 2009, Pages 10-21

  Schnyder, Andreas P ^a   Ryu, Shinsei ^b   Furusaki, Akira ^c   Ludwig, Andreas W W ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c RIKEN   (Japan)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Anderson localization; Quantum hall effects; Topological phase

Indexed keywords

EID: 65649114938     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.3149481     Document Type: Conference Paper

References (39)

1. Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas W. W. Ludwig, Phys. Rev. B 78, 195125 (2008); see also "Anderson Localization at Boundaries: Classification of Topological Insulators and Superconductors", http://landaulOO.itp.ac.ru/Talk;s/ludwig.pdL
2. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).
3. E. Witten, Commun. Math. Phys. 121, 351 (1989).
4. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991).
5. Y. Hatsugai, Phys. Rev. Lett. 7, 3697 (1993).
6. E. Witten, arXiv:0706.3359 (unpubUshed).
7. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005); 95, 226801 (2005). B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. 96, 106802 (2006).
8. M. Konig, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, J. Phys. Soc. Jpn. 77, 031007(2008).
9. M. König, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. Mohlenkamp, X.-L. Qi, and S.-C. Zhang, Science 314, 1757 (2006).
10. J. E. Moore and L. Balents, Phys. Rev. B 75, 121306(R) (2007).
11. Rahul Roy, arXiv:cond-mat/0607531 (unpublished).20
12. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
13. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. Hor, R. Cava, and M. Hasan, Nature 452, 970 (2008).
14. D. Hsieh, Y Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, R Meier, G. Bihknayer, C. L. Kane, Y S. Hor, R. J. Cava, and M. Z. Hasan, Science 323, 919 (2009).
15. M. R. Zirnbauer, Phys. Rev. Lett. 69, 1584 (1992); A. D. Mirlin, A. MuUer-Groeling, and M. R. Zirnbauer, Ann. Phys. (N.Y) 236, 325 (1994).
16. A. Yu. Kitaev, "Periodic table for topological insulators and superconductors", this Volume; arXiv:0901.2686; see also "Periodic Table for Topological Insulators and Superconductors", http ://landau 100. itp. ac .ru/TaUcs/kitaev.pdf.
17. M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996).
18. A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997).
19. See, e.g., also a more recent treatment: P. Heinzner, A. Huck Leberry, and M. R. Zirnbauer, Commun. Math. Phys. 257, 725 (2005).
20. F. J. Dyson, J. Math. Phys. 3, 1199 (1962); M. L. Mehta, Random Matrices, Academic Press, Boston, 1991.
21. G. E. Volovik, in The Universe in a Helium Droplet, The International Series of Monographs on Physics Vol. 117, Oxford University Press, New York, 2003; G. E. Volovik, in Exotic Properties of Superfluid 3He, Series I N Modern Condensed Matter Physics Vol. 1, World Scientific, Singapore, 1992.
22. Andreas P. Schnyder, Shinsei Ryu, and Andreas W.W. Ludwig, arXiv:0901.1343 (unpubUshed).
23. K. Efetov, Supersymmetry in Disorder and Chaos, Cambridge University Press, Cambridge, England, 1997.
24. B. DeWitt, Supermanifolds, Cambridge University Press, Cambridge, England, 1992.
25. M. Kohmoto, B. I. Halperin, and Y S. Wu, Phys. Rev. B 45, 13488 (1992).
26. A. Pruisken, Nucl. Phys. B 235, 277 (1984).
27. C. G. Callan, Jr. and J. A. Harvey, Nucl. Phys. B 250, 427 (1985).
28. R D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
29. A. W. W. Ludwig, M. P A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).
30. D. Bernard and A. LeClair, J. Phys. A 35, 2555 (2002).
31. T. Ando and T. Nakanishi, J. Phys. Soc. Jpn. 67, 1704 (1998); T. Ando, T. Nakanishi, and R. Saito, ibid. 67, 2857 (1998).
32. S. Ryu, C. Mudry, H. Obuse, and A. Furusaki, Phys. Rev. Lett. 99, 116601 (2007).
33. K. Nomura, M. Koshino, and S. Ryu, Phys. Rev. Lett. 99, 146806 (2007).
34. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. 98, 256801 (2007).
35. J. H. Bardarson, J. Tworzydlo, P. W. Brouwer, and C. W. J. Beenakker, Phys. Rev. Lett. 99, 106801 (2007).
36. A. M. Tsvelik, Phys. Rev. B 51, 9449 (1995).
37. C. Mudry, C. Chamon, and X.-G. Wen, Nucl. Phys. B 466, 383 (1996).
38. M. J. Bhaseen, J.-S. Caux, 1.1. Kogan, and A. M. Tsvelik, Nucl. Phys. B 618, 465 (2001).
39. A. W. W. Ludwig, arXiv:cond-maf0012189 (unpublished).