Quasiparticle Hall transport of d-wave superconductors in the vortex state

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 22, 2001, Pages

  Vafek, O ^a   Melikyan, A ^a   Tesanovic Z ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ARTICLE; ATOMIC PARTICLE; CALCULATION; PHYSICS; QUANTUM MECHANICS; SEMICONDUCTOR; THERMAL CONDUCTIVITY;

EID: 0035606020     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.224508     Document Type: Article

References (60)

1. D. J. Van Harlingen, Rev. Mod. Phys. 67, 515 (1995).
2. J. Orenstein and A. J. Millis, Science 288, 468 (2000).
3. M. B. Walker and M. F. Smith, Phys. Rev. B 61, 11 285 (2000).
4. H. Ding, M. R. Norman, J. C. Campuzano, M. Raderia, A. F. Bellman, T. Yokoya, T. Takahashi, T. Mochiku, and K. Kadowaki, Phys. Rev. B 54, R9678 (1996).
5. M. Chiao, R. W. Hill, C. Lupien, L. Taillefer, P. Lambert, R. Gagnon, and P. Fournier, cond-mat/9910367 (unpublished).
6. Y. Zhang, N. P. Ong, P. W. Anderson, D. A. Bonn, R. Liang, and W. N. Hardy, Phys. Rev. Lett. 86, 890 (2001).
7. S. H. Simon and P. A. Lee, Phys. Rev. Lett. 78, 1548 (1997).
8. L. P. Gor’kov and J. R. Schrieffer, Phys. Rev. Lett. 80, 3360 (1998).
9. P. W. Anderson, cond-mat/9812063 (unpublished).
10. E. J. Ferrer, V. P. Gusynin, and V. de la Incera, hep-ph/0101308 (unpublished).
11. N. B. Kopnin and V. M. Vinokur, Phys. Rev. B 62, 9770 (2000).
12. M. Franz and Z. Tešanović, Phys. Rev. Lett. 84, 554 (2000).
13. L. Marinelli, B. I. Halperin, and S. H. Simon, Phys. Rev. B 62, 3488 (2000).
14. A. S. Melnikov, J. Phys.: Condens. Matter 82, 4703 (1999).
15. D. Knapp, C. Kallin, and A. J. Berlinsky, cond-mat/0011053 (unpublished).
16. O. Vafek, A. Melikyan, M. Franz, and Z. Tešanović, Phys. Rev. B 63, 134509 (2001).
17. Y. Wang and A. H. MacDonald, Phys. Rev. B 52, R3876 (1995).
18. K. Yasui and T. Kita, Phys. Rev. Lett. 83, 4168 (1999).
19. We wish to alert the reader to the new preprint by A. Vishwanath, cond-mat/0104213 (unpublished), where some of the results reported in our paper have been independently derived. While our approaches are different, the results appear to be in general agreement where applicable and the two papers could be considered complementary. We direct the reader’s attention to an elegant discussion in cond-mat/0104213 (unpublished) of symmetry properties of quasiparticle spectra which has helped us in our own work (see Sec. V), and, in particular, to the issue of protection of Dirac nodes discussed there.
20. J. Ye, Phys. Rev. Lett. 86, 316 (2001).
21. M. Nielsen and P. Hedegård, Phys. Rev. B 51, 7679 (1995).
22. T. Senthil, M. P. A. Fisher, L. Balents, and C. Nayak, cond-mat/9808001 (unpublished).
23. Quantized spin currents in superfluids and superconductors in different physical situations have also been considered in G. E. Volovik, JETP Lett. 66, 522 (1997)
24. and G. E. Volovik and V. M. Yakovenko, J. Phys.: Condens. Matter 1, 5263 (1989).
25. See also V. M. Yakovenko, Phys. Rev. Lett. 65, 251 (1990).
26. A. C. Durst and P. A. Lee, Phys. Rev. B 62, 1270 (2000).
27. This quantization is an example of a general class of problems exhibiting the “parity anomaly” as originally discussed in F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
28. For application to spin currents in chiral magnets see F. D. M. Haldane and D. P. Arovas, Phys. Rev. B 52, 4223 (1995). For various manifestations of such quantized transport in superfluids and superconductors see Refs. 2223.
29. For translationally invariant superconductors with broken time-reversal and parity such topological invariant has been derived by N. Read and Dmitry Green, Phys. Rev. B 61, 10 267 (2000).
30. In a typical situation, the combined symmetry of BdG equations and the inversion symmetry of a vortex lattice conspire to restrict (Formula presented) to even multiples of ħ/8π.
31. For discussion of some general properties of the BCS–Hofstadter problem in d-wave superconductors see Y. Morita and Y. Hatsugai, cond-mat/0007067 (unpublished).
32. In real superconductors, this sequence of transitions will also be influenced by strong disorder. For spin QHE in dirty superconductors with broken orbital time-reversal symmetry see I. A. Gruzberg, A. W. Ludwig, and N. Read, Phys. Rev. Lett. 82, 4524 (1999)
33. Phys. Rev. Lett.V. Kagalovsky, B. Horovitz, Y. Avishai, and J. T. Chalker, 82, 3516 (1999). In our case, perhaps the most interesting and relevant form of disorder is the one associated with disorder in vortex positions.
34. P. G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, Reading, MA, 1989).
35. T. Senthil, J. B. Marston, and M. P. A. Fisher, cond-mat/9902062 (unpublished).
36. J. M. Luttinger, Phys. Rev. A 135, 1505 (1964).
37. Yu. N. Obraztsov, Fiz. Tverd. Tela (Leningrad) 6, 414 (1964) [Sov. Phys. Solid State 6, 331 (1964)]
38. Sov. Phys. Solid StateYu. N. Obraztsov7, 455 (1965).
39. L. Smrčka and P. Středa, J. Phys. C 10, 2153 (1977).
40. H. Oji and P. Streda, Phys. Rev. B 31, 7291 (1985).
41. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1990).
42. M. Kohmoto, Ann. Phys. (N.Y.) 160, 343 (1985).
43. M. Jonson and S. M. Girvin, Phys. Rev. B 29, 1939 (1984).
44. J. von Neumann and E. Wigner, Phys. Z. 30, 467 (1927).
45. M. Reed and B. Simon, Fourier Analysis and Self-Adjointess (Academic, New York, 1975).
46. R. Richtmyer, Principles of Advanced Mathematical Physics, Vol. I (Springer-Verlag, New York, 1978).
47. P. de Sousa Gerbert, Phys. Rev. D 40, 1346 (1989).
48. P. de Sousa Gerbert and R. Jackiw, Commun. Math. Phys. 124, 229 (1989).
49. Y. A. Sitenko and D. G. Rakityanskii, Phys. At. Nucl. 60, 1497 (1997).
50. C. Manuel and R. Tarrash, Phys. Lett. B 301, 72 (1993).
51. M. G. Alford, J. March-Russell, and F. Wilczek, Nucl. Phys. B 328, 140 (1989)
52. C. R. Hagen, Phys. Rev. Lett. 64, 503 (1990)
53. E. G. Flekkøy and J. M. Leinaas, Int. J. Mod. Phys. A 6, 5327 (1991)
54. V. D. Skarzhinsky and J. Audretsch, J. Phys. A 30, 7603 (1997)
55. C. G. Beneventano, M. De Francia, and E. M. Santangelo, Int. J. Mod. Phys. A 14, 4749 (1999).
56. M. Franz and Z. Tešanović, Phys. Rev. Lett. 80, 4763 (1998).
57. S. Dukan and Z. Tešanović, Phys. Rev. B 49, 13 017 (1994)
58. Z. Tešanović and P. Sacramento, Phys. Rev. Lett. 80, 1521 (1998).
59. C. Poole, Jr., H. A. Farach, and R. J. Creswick, Superconductivity (Academic, San Diego, 1995).
60. V. Ambegaokar and A. Griffin, Phys. Rev. 137, A1151 (1965).