Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff

Abstract

In this paper we discuss the Eliashberg equations for the case of an electron-phonon coupling with an energy cutoff. This cutoff is imposed either for the energy difference by means of a strip function, or for both energies, with a Cooper-like expression. The strip function cutoff requires explicit calculation of not only the frequency renormalization functionZ but also the energy renormalizationX. The physical origin of such cutoffs might lie in the very strong electron-electron interaction which seems typical for highTc superconductivity. If such cutoffs are admitted, the hypothesis thatTc is caused at least in part by a strong electron-phonon interaction can be reconsidered. We find that the combination of strong coupling and low-energy cutoff could produce highTc with only small isotope effect and with little damping or pulling of the phonon modes. Correlation with other physical properties, such as specific heat, is reexamined in view to estimate the coupling constant λ. Some objections to the model using strong electron phonon interaction are removed and better agreement with observed properties is obtained