Ward identity and optical conductivity sum rule in the d-density wave state

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 10, 2005, Pages

  Benfatto, L ^a   Sharapov, S G ^b   Andrenacci, N ^c   Beck, H ^c  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b ISI FOUNDATION   (Italy)

^c UNIVERSITY OF NEUCHÂTEL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONDUCTANCE; CORRELATION ANALYSIS; DENSITY; ELECTRIC CURRENT; ENERGY; MICROSCOPY; MODEL; OPTICS; SUPERCONDUCTOR;

EID: 20344369535     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.104511     Document Type: Article

References (56)

1. H. J. A. Molegraaf, C. Presura, D. van der Marel, P. H. Kes, and M. Li, Science 295, 2239 (2002).
2. A. F. Santander-Syro, R. P. S. M. Lobo, N. Bontemps, Z. Konstantinovic, Z. Z. Li, and H. Raffy, Phys. Rev. Lett. 88, 097005 (2002);
3. Europhys. Lett. 62, 568 (2003).
4. C. C. Homes, S. V. Dordevic, D. A. Bonn, Ruixing Liang, and W. N. Hardy, Phys. Rev. B 69, 024514 (2004).
5. A. F. Santander-Syro, R. P. S. M. Lobo, and N. Bontemps, condmat/0404290 (unpublished), to appear in NATO Advanced Research Workshop Proceedings, 2005.
6. A. V. Boris, N. N. Kovaleva, O. V. Dolgov, T. Holden, C. T. Lin, B. Keimer, and C. Bernhard, Science 304, 708 (2004).
7. M. Ortolani, P. Calvani, and S. Lupi, cond-mat/0407432, Phys. Rev. Lett. (to be published).
8. J. Jaklič and P. Prelovšek, Adv. Phys. 49, 1 (2000).
9. A. J. Millis, in Strong Interactions in Low Dimensions, edited by D. Baeriswyl and L. De Giorgi (Kluver Academic, Berlin, 2003).
10. D. van der Marel, Interaction electrons in low dimensions, book series Physics and Chemistry of Materials with Low-Dimensional Structures (Kluwer Academic, Berlin, 2003); condmat/0301506 (unpublished).
11. P. F. Maldague, Phys. Rev. B 16, 2437 (1977).
12. D. Baeriswyl, C. Gros, and T. M. Rice, Phys. Rev. B 35, 8391 (1987).
13. D. J. Scalapino, S. R. White, and S. Zhang, Phys. Rev. B 47, 7995 (1993).
14. See L. B. Ioffe and A. J. Millis, Science 285, 124 (1999) and references therein.
15. J. E. Hirsch and F. Marsiglio, Phys. Rev. B 62, 15 131 (2000).
16. M. R. Norman and C. Pépin, Phys. Rev. B 66, 100506 (2002).
17. T. Eckl, W. Hanke, and E. Arrigoni, Phys. Rev. B 68, 014505 (2003).
18. A. Knigavko, J. P. Carbotte, and F. Marsiglio, Phys. Rev. B 70, 224501 (2004).
19. V. M. Loktev, R. M. Quick, and S. G. Sharapov, Phys. Rep. 349, 1 (2001).
20. B. I. Halperin and T. M. Rice, Solid State Phys. 21, 115 (1968).
21. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988).
22. A. A. Nersesyan and G. E. Vachanadze, J. Low Temp. Phys. 77, 293 (1989).
23. H. J. Schulz, Phys. Rev. B 39, 2940 (1989).
24. C. M. Varma, Phys. Rev. B 55, 14 554 (1997).
25. M. V. Eremin and I. A. Larionov, Pis'ma Zh. Eksp. Teor. Fiz. 68, 583 (1998);
26. [JETP Lett. 68, 611 (1998)].
27. E. Cappelluti and R. Zehyer, Phys. Rev. B 59, 6475 (1999).
28. L. Benfatto, S. Caprara, and C. Di Castro, Eur. Phys. J. B 17, 95 (2000).
29. S. Chakravarty, R. B. Laughlin, D. K. Morr, and C. Nayak, Phys. Rev. B 63, 094503 (2001).
30. C. Castellani, C. Di Castro, and M. Grilli, Phys. Rev. Lett. 75, 4650 (1995);
31. C. Di Castro, L. Benfatto, S. Caprara, C. Castellani, and M. Grilli, Physica C 341-348, 1715 (2000).
32. V. Vescoli, L. Degiorgi, H. Berger, and L. Forró, Phys. Rev. Lett. 81, 453 (1998).
33. A. H. Castro Neto, Phys. Rev. Lett. 86, 4382 (2001).
34. L. Benfatto, S. Sharapov, and H. Beck, Eur. Phys. J. B 39, 469 (2004).
35. Y. Nambu, Phys. Rev. 117, 648 (1960).
36. J. R. Schrieffer, Theory of Superconductivity (Addison-Wesley, New York, 1988).
37. Q.-H. Wang, J. H. Han, and D.-H. Lee, Phys. Rev. Lett. 87, 077004 (2001).
38. J.-X. Zhu, W. Kim, C. S. Ting, and J. P. Carbotte, Phys. Rev. Lett. 87, 197001 (2001).
39. H.-Y. Kee and Y. B. Kim, Phys. Rev. B 66, 052504 (2002).
40. X. Yang and C. Nayak, Phys. Rev. B 65, 064523 (2002).
41. S. Chakravarty, C. Nayak, S. Tewari, and X. Yang, Phys. Rev. Lett. 89, 277003 (2002).
42. S. G. Sharapov, V. P. Gusynin, and H. Beck, Phys. Rev. B 67, 144509 (2003).
43. D. N. Aristov and R. Zeyher, Phys. Rev. B 70, 212511 (2004); cond-mat/0406419 (unpublished).
44. B. Valenzuela, E. J. Nicol, and J. P. Carbotte, cond-mat/0407497 (unpublished).
45. C. P. Enz, A Course on Many-Body Theory Applied to Solid-State Physics (World Scientific, Singapore, 1992).
46. F. However, since in the following we are interested in discussing the optical conductivity, which is related to the q=0 limit of the current operator (2.16), we can adopt the notation (2.14)-(2.16) without loss of generality.
47. V. P. Gusynin and V. A. Miransky, Mod. Phys. Lett. A 6, 2443 (1991);
48. Sov. Phys. JETP 74, 216 (1992).
49. J. S. Langer, Phys. Rev. 127, 5 (1962).
50. k+Qσ+h.c. should be considered instead.
51. A. Lucarelli, S. Lupi, M. Ortolani, P. Calvani, P. Maselli, M. Capizzi, P. Giura, H. Eisaki, N. Kikugawa, T. Fujita, M. Fujita, and K. Yamada, Phys. Rev. Lett. 90, 037002 (2003);
52. C. Bernhard, T. Holden, A. V. Boris, N. N. Kovaleva, A. V. Pimenov, J. Humlicek, C. Ulrich, C. T. Lin, and J. L. Tallon, Phys. Rev. B 69, 052502 (2004).
53. S. Caprara, C. Di Castro, S. Fratini, and M. Grilli, Phys. Rev. Lett. 88, 147001 (2002).
54. L. Benfatto and C. Morais Smith, Phys. Rev. B 68, 184513 (2003).
55. A. Toschi, M. Capone, C. Castellani, M. Ortolani, and P. Calvani (unpublished).
56. A. Ino, C. Kim, M. Nakamura, T. Yoshida, T. Mizokawa, A. Fujimori, Z.-X. Shen, T. Kakeshita, H. Eisaki, and S. Uchida, Phys. Rev. B 65, 094504 (2002).