The ratio 2Δ/Tc in Eliashberg theory

Journal of Low Temperature Physics

Volumn 102, Issue 1-2, 1996, Pages 193-225

  Combescot, R ^a   Varelogiannis, G ^a,b  

^a SORBONNE UNIVERSITÉ   (France)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2842538873     PISSN: 00222291     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf00755117     Document Type: Article

References (31)

1. For reviews of the weak and the strong coupling theories of superconductivity, see for example Superconductivity, ed. by R. D. Parks (Dekker, N.Y., 1969)
2. B. Mitrovic, H. G. Zarate, and J. P. Carbotte, Phys. Rev. B 29, 184 (1984).
3. c Superconductivity III, ed, by M. Tachiki, Y. Muto, and Y. Syono (North Holland, 1991)
4. c Superconductivity IV (1994, North Holland).
5. J. R. Schrieffer, X. G. Wen, and S. C. Zhang, Phys. Rev. Lett. 60, 944 (1988)
6. Phys. Rev. B 39, 11663 (1989);
7. A. Kampf and J. R. Schrieffer, Phys. Rev. B 41, 6399 (1990)
8. Phys. Rev. B 42, 7967 (1990).
9. P. Monthoux, A. V. Balatsky, and D. Pines, Phys. Rev. Lett. 67, 3448 (1991).
10. C. M. Varma, P. B. Littlewood, S. Schmitt-Rink, E. Abrahams, and A. E. Ruckenstein, Phys. Rev. Lett. 63, 1996 (1989).
11. For a review of the present situation, see J. P. Carbotte, Rev. Mod. Phys. 62, 1027 (1990).
12. See for example D. Rainer, Progr. in Low Temp. Phys. X, ed. D. F. Brewer, and P. B. Allen, and B. Mitrovic, Sol. State Phys. 37 , ed. F. Seitz, D. Turnbull, and H. Ehrenreich (Academic, N.Y., 1982).
13. This is also our estimated numerical precision in this work (although many of our calculations have a much better precision). When on some occasions we quote errors of order 1% or below, we mean relative errors between calculations made in the same conditions.
14. R. Combescot, Phys. Rev. Lett. 67, 148 (1991).
15. B. T. Geilikman and V. Z. Kresin, Fiz. Tverd. Tela (Leningrad) 1, 3294 (1965)
16. [Sov. Phys. Solid State 7, 2659 (1966)].
17. J. M. Coombes and J. P. Carbotte, J. Low Temp. Phys. 63, 431 (1986).
18. R. Combescot and G. Varelogiannis, Sol. State Comm. 93, 113 (1995).
19. W. Weber, Phys. Rev. Lett. 58, 1371 and 2154(E) (1987).
20. F. Marsiglio, M. Schossmann, and J. P. Carbotte, Phys. Rev. B 37, 4965 (1988).
21. 3/2 which is analytical. The coefficients in the expansions themselves are obtained by comparison with the numerical results. In this respect the large λ limit of 11.8 which we give here is 7% below the precise result of 12.6 obtained in the very large λ limit by F. Marsiglio and J. P. Carbotte, Phys. Rev. B 43, 5355 (1991)
22. (see also J. P. Carbotte, F. Marsiglio, and B. Mitrovic, Phys. Rev. B 33, 6135 (1986)). This slight discrepancy is due to the slow variation of Δ with λ in this range and does not imply numerical disagreement with their work. Actually our coefficients give a very precise agreement with our numerical results, up to λ = 25, as indicated in Sec. VI, but also agree with their results within 1% for λ = 100.
23. G. Bergmann and D. Rainer, Z. Phys. 263, 59 (1973).
24. B. Batlogg in the Proceedings of LT19, Physica B 169, 7 (1991)
25. A. F. Hebard, Physics Today, Nov. 1992, p. 26.
26. Z. Zhang, C. Chen, and C. M. Lieber, Science 254, 1619 (1991).
27. C. M. Varma, J. Zaanen, and K. Raghavachari, Science 254, 989 (1991).
28. F. C. Zhang, M. Ogata, and T. M. Rice, Phys. Rev. Lett. 67, 3452 (1991).
29. c is calculated exactly from the linear Eliashberg equations.
30. This formula has actually been proposed, but not explored in R. Combescot, Europhys. Lett. 10, 177 (1989).
31. B. Mitrovic, C. R. Leavens, and J. P. Carbotte, Phys. Rev. B 21, 5048 (1980).