Superconductivity and Abelian chiral anomalies

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 5, 2004, Pages

  Hatsugai, Y ^a   Ryu, S ^a   Kohmoto, M ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHIRALITY; CRYSTAL STRUCTURE; ELECTRIC CONDUCTIVITY; GEOMETRY; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS; SUPERCONDUCTOR;

EID: 19544387912     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.054502     Document Type: Article

References (36)

1. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
2. T. Eguchi, P. B. Gilkey, and A. J. Hanson, Phys. Rep. 66, 213 (1980).
3. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
4. D. J. Thouless, M. Kohmoto, P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
5. M. Kohmoto, Ann. Phys. (N.Y.) 160, 355 (1985).
6. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
7. X. G. Wen, Phys. Rev. B 40, 7387 (1989).
8. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).
9. Y. Hatsugai, Phys. Rev. B 48, 11 851 (1993).
10. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
11. Y. Hatsugai, J. Phys.: Condens. Matter 9, 2507 (1997).
12. S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002).
13. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988).
14. T. Senthil, J. B. Marston, and M. P. A. Fisher, Phys. Rev. B 60, 4245 (1999).
15. Y. Morita and Y. Hatsugai, Phys. Rev. B 62, 99 (2000).
16. O. Vafek, A. Melikyan, and Z. Tesanovic, Phys. Rev. B 64, 224508 (2001).
17. 25
18. Y. Hatsugai and S. Ryu, Phys. Rev. B 65, 212510 (2002).
19. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931).
20. B. I. Halperin, Jpn. J. Appl. Phys., Suppl. 26, 1913 (1987).
21. M. Kohmoto, B. I. Halperin, and Y. S. Wu, Phys. Rev. B 45, 13 488 (1992).
22. 12 associated with a breaking of a time-reversal symmetry are discussed in Refs. 23 and 24.
23. K. Izawa, Y. Nakajima, J. Goryo, Y. Matsuda, S. Osaki, H. Sugawara, H. Sato, P. Thalmeier, and K. Maki, Phys. Rev. Lett. 90, 117001 (2003).
24. Y. Aoki, A. Tuschiya, T. Kanayama, S. R. Saha, H. Sugawara, H. Sato, W. Higemoto, A. Koda, K. Ohishi, and K. Nishiyama, Phys. Rev. Lett. 91, 067003 (2003).
25. 3He (World Scientific, Singapore, 1992).
26. G. E. Volovik and L. P. Gor'kov, Sov. Phys. JETP 61, 843 (1985).
27. M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).
28. μ runs over [0, π] to avoid double counting.
29. F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
30. B. Zumino, Current Algebra and Anomaly (World Scientific, Singapore, 1991), p. 362.
31. Y. Hatsugai and S. Ryu, Physica C 388, 90 (2003).
32. Y. Hatsugai and M. Kohmoto (unpublished).
33. j, i, j=0, . . ., 3.
34. It is a similar procedure to fix phases of states for nondegenerate cases.
35. λU) = 0. It also completes a general proof of the sum rule for the nondegenerate states, that is, the sum of the Chern numbers for all bands is zero.
36. 0. Another base which diagonalizes d·σ is also useful.