Effect of Umklapp Scattering on Magnetic Field Penetration Depth in High-Tc Cuprates

Journal of the Physical Society of Japan

Volumn 71, Issue 3, 2002, Pages 888-904

  Jujo, Takanobu ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Antiferromagnetic spin fluctuation; Current of quasiparticles; Electron electron correlation; Fermi liquid theory; High Tc cuprates; Magnetic field penetration depth; Perturbation theory; Umklapp scattering; Vertex correction

Indexed keywords

COPPER;

ARTICLE; CALCULATION; DENSITY; ELECTRON; ELEMENTARY PARTICLE; MAGNETISM; MATHEMATICAL ANALYSIS; THEORY; VELOCITY;

EID: 0036246006     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.71.888     Document Type: Article

References (45)

1. H. Takagi, T. Ito, S. Ishibashi, M. Uota, S. Uchida and Y. Tokura: Phys. Rev. B 40 (1989) 2254.
2. J. Takeda, T. Nishikawa and M. Sato: Physica C 231 (1994) 293.
3. Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. Kiefl, S. R. Kreitzman, P. Mulhern, T. M. Riseman, D. Ll. Williams, B. X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan, A. W. Sleight, M. A. Subramanian, C. L. Chien, M. Z. Cieplak, Gang Xiao, V. Y. Lee, B. W. Statt, C. E. Stronach, W. J. Kossler and X. H. Yu: Phys. Rev. Lett. 62 (1989) 2317.
4. V. J. Emery and S. A. Kivelson: Nature 374 (1995) 434.
5. T. Moriya, Y. Takahashi and K. Ueda: J. Phys. Soc. Jpn. 59 (1990) 2905.
6. H. Kohno and K. Yamada: Prog. Theor. Phys. 85 (1991) 13.
7. T. Jujo and K. Yamada: J. Phys. Soc. Jpn. 68 (1999) 2198; T. Jujo, Y. Yanase and K. Yamada: ibid. 69 (2000) 2240.
8. T. Jujo and K. Yamada: J. Phys. Soc. Jpn. 68 (1999) 2198; T. Jujo, Y. Yanase and K. Yamada: ibid. 69 (2000) 2240.
9. S. Koikegami and K. Yamada: J. Phys. Soc. Jpn. 69 (2000) 768;
10. Y. Yanase and K. Yamada: ibid. 70 (2001) 1659.
11. H. Kontani, K. Kanki and K. Ueda: Phys. Rev. B 59 (1999) 14723;
12. K. Kanki and H. Kontani: J. Phys. Soc. Jpn. 68 (1999) 1614.
13. L. D. Landau: Sov. Phys. JETP 3 (1957) 920; ibid. 5 (1959) 101; ibid. 8 (1959) 70.
14. L. D. Landau: Sov. Phys. JETP 3 (1957) 920; ibid. 5 (1959) 101; ibid. 8 (1959) 70.
15. L. D. Landau: Sov. Phys. JETP 3 (1957) 920; ibid. 5 (1959) 101; ibid. 8 (1959) 70.
16. P. A. Lee and X.-G. Wen: Phys. Rev. Lett. 78 (1997) 4111.
17. D. L. Feng, D. H. Lu, K. M. Shen, C. Kim, H. Eisaki, A. Damascelli, R. Yoshizaki, J.-i. Shimoyama, K. Kishio, G. D. Gu, S. Oh, A. Andrus, J. O'Donnell, J. N. Eckstein and Z.-X. Shen: Science 289 (2000) 277.
18. A. J. Leggett: Phys. Rev. 140 (1965) A1869.
19. A. J. Millis, S. M. Girvin, L. B. Ioffe and A. I. Larkin: J. Phys. Chem. Solids 59 (1998) 1742.
20. T. Jujo: J. Phys. Soc. Jpn. 70 (2001) 1349.
21. K. Kanki and K. Yamada: J. Phys. Soc. Jpn. 66 (1997) 1103.
22. H. Maebashi and H. Fukuyama: J. Phys. Soc. Jpn. 66 (1997) 3577.
23. T. Okabe: J. Phys. Soc. Jpn. 67 (1998) 2792.
24. D. Pines and P. Noziéres: The Theory of Quantum Liquids I (W. A. Benjamin, New York, 1966).
25. K. Kadowaki and S. B. Woods: Solid State Commun. 58 (1986) 507.
26. P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham and J. W. Wilkins: Comments Condens. Matter Phys. 12 (1986) 99.
27. K. Yamada and K. Yosida: Prog. Theor. Phys. 76 (1986) 621.
28. A. A. Abrikosov, L. P. Gor'kov and I. E. Dzyaloshinskii: Methods of Quantum Field Theory in Statistical Physics (Pergamon, Oxford, 1965).
29. For example, J. R. Schrieffer: Theory of Superconductivity (W. A. Benjamin, New York, 1964).
30. T. Okabe: J. Phys. Soc. Jpn. 67 (1998) 4178.
31. P. Noziéres: Theory of Interacting Fermi Systems (W. A. Benjamin, New York, 1964).
32. G. Baym and L. P. Kadanoff: Phys. Rev. 124 (1961) 287; G. Baym: ibid. 127 (1962) 1391.
33. G. Baym and L. P. Kadanoff: Phys. Rev. 124 (1961) 287; G. Baym: ibid. 127 (1962) 1391.
34. S. Koikegami, S. Fujimoto and K. Yamada: J. Phys. Soc. Jpn. 66 (1997) 1438.
35. T. Takimoto and T. Moriya: J. Phys. Soc. Jpn. 67 (1998) 3570.
36. M. Eschrig and M. R. Norman: Phys. Rev. Lett. 85 (2000) 3261.
37. V. Barzykin and D. Pines: Phys. Rev. B 52 (1995) 13585.
38. J. Mesot, M. R. Norman, H. Ding, M. Randeria, J. C. Campuzano, A. Paramekanti, H. M. Fretwell, A. Kaminski, T. Takeuchi, T. Yokoya, T. Sato, T. Takahashi, T. Mochiku and K. Kadowaki: Phys. Rev. Lett. 83 (1999) 840.
39. C. Panagopoulos, B. D. Rainford, J. R. Cooper, W. Lo, J. L. Tallon, J. W. Loram, J. Betouras, Y. S. Wang and C. W. Chu: Phys. Rev. B 60 (1999) 14617.
40. ω is difficult to derive and its property is not trivial because this is the solution of the integral equation for the four-point vertex. This is the reason why we derive the formula which shows that the two integral equations for the three-point vertex is sufficient to obtain the expression for the current. Therefore their formula is incorrect.
41. ω is difficult to derive and its property is not trivial because this is the solution of the integral equation for the four-point vertex. This is the reason why we derive the formula which shows that the two integral equations for the three-point vertex is sufficient to obtain the expression for the current. Therefore their formula is incorrect.
42. K. Yamada: Prog. Theor. Phys. 53 (1975) 970.
43. M. Imada, A. Fujimori and Y. Tokura: Rev. Mod. Phys. 70 (1998) 1039.
44. Y. M. Vilk and A.-M. S. Tremblay: J. Phys. I (France) 7 (1997) 1309.
45. G. M. Éliashberg: Sov. Phys. JETP 14 (1962) 886.