Journal of Low Temperature Physics

, Volume 87, Issue 5–6, pp 659–682

Eliashberg theory of the critical temperature and isotope effect. Dependence on bandwidth, band-filling, and direct Coulomb repulsion

  • F. Marsiglio

We investigate the dependence of the superconducting critical temperature and the isotope coefficient on bandwidth, band-filling, and the direct Coulomb repulsion, within Eliashberg theory. The Migdal approximation is assumed throughout, and the Coulomb repulsion is modelled by the Hubbard U and treated in the simplest approximation. We assume a constant density of states with a finite bandwidth. We find that while, in principle, small isotope coefficients are possible, it is unlikely that the isotope coefficient can ever be negative within this model. Furthermore, it is difficult to achieve small isotope coefficients for realistic parameters. Finally, we discuss a possible means by which large isotope coefficients can occur at low filling.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    For a review of isotope effect measurements, see: J. P. Carbotte, On the Isotope Effect, to be published in Proceedings of Symposium on the Manifestations of the Electron-Phonon Interaction in CuO and Related Superconductors, R. Baquero, ed. (World Scientific, Singapore, 1991).Google Scholar
  2. 2.
    M. K. Crawford et al., Phys. Rev. B 41, 283 (1990).Google Scholar
  3. 3.
    J. P. Franck, et al., Physica B 169, 697 (1991).Google Scholar
  4. 4.
    E. Schachinger, M. G. Greeson, and J. P. Carbotte, Phys. Rev. B 42, 406 (1990).Google Scholar
  5. 5.
    R. Akis and J. P. Carbotte, Phys. Rev. B 41, 11661 (1990).Google Scholar
  6. 6.
    C. C. Tsuei et al., Phys. Rev. Lett. 65, 2724 (1990).Google Scholar
  7. 7.
    J. P. Carbotte, M. Greeson, and A. Perez-Gonzalez, Phys. Rev. Lett. 66, 1789 (1991).Google Scholar
  8. 8.
    J. C. Swihart, Phys. Rev. 116, 45 (1959).Google Scholar
  9. 9.
    J. Labbé and J. Friedel, J. Phys. Radium 27, 153 (1966); J. Labbé, S. Barisic, and J. Friedel, Phys. Rev. Lett. 19, 1039 (1967).Google Scholar
  10. 10.
    P. Morel and P. W. Anderson, Phys. Rev. 125, 1263 (1962).Google Scholar
  11. 11.
    J. W. Garland Jr., Phys. Rev. Lett. 11, 114 (1963).Google Scholar
  12. 12.
    J. P. Carbotte (private communication).Google Scholar
  13. 13.
    N. N. Bogoliubov, N. V. Tolmachev, and D. V. Shirkov, A New Method in the Theory of Superconductivity (Consultants Bureau, New York, 1959).Google Scholar
  14. 14.
    T. Holstein, Ann. Phys. 8, 325 (1959).Google Scholar
  15. 15.
    J. Hubbard, Proc. Roy. Soc. A 276 238 (1963).Google Scholar
  16. 16.
    D. J. Thouless, Ann. Phys. 10, 553 (1960).Google Scholar
  17. 17.
    See, for example, P. B. Allen and B. Mitrović, in Solid State Physics, H. Ehrenreich, F. Seitz, and D. Turnbull, eds. (Academic Press, New York, 1982), Vol. 37, p. 1.Google Scholar
  18. 18.
    J. P. Carbotte, Rev. Mod. Phys. 62, 1027 (1990).Google Scholar
  19. 19.
    F. Marsiglio, Physica C 160, 305 (1989).Google Scholar
  20. 20.
    C. S. Owen and D. J. Scalapino, Physica 55, 691 (1971).Google Scholar
  21. 21.
    G. Bergmann and D. Rainer, Z. Physik 263, 59 (1973).Google Scholar
  22. 22.
    J. E. Hirsch first suggested this possibility to the author, in the context of temperature dependent Hall coefficient calculations.Google Scholar
  23. 23.
    J. Kanamori, Prog. Theor. Phys. 30, 275 (1963). More recently, see H. Fukuyama and Y. Hasegawa, Prog. Theor. Phys. (Suppl.) 101, 441 (1990), and L. Chen, C. Bourbonnais, T. Li, and A.-M. S. Tremblay, Phys. Rev. Lett. 66, 369 (1991).Google Scholar
  24. 24.
    D. Rainer and F. J. Culetto, Phys. Rev. B 19, 2540 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • F. Marsiglio
    • 1
  1. 1.Theoretical Physics Branch, AECL Research, Chalk River LaboratoriesChalk RiverCanada

Personalised recommendations