Some consequences of the breakdown of Migdal's theorem in high-T-c superconductors

In order to reproduce the experimental T-c and tunneling data of high-T-c s uperconductors in the framework of the Eliashberg theory for strong electro n-boson interaction, it is necessary to use large values of the coupling co nstant. In this work, we investigate whether this fact is a possible conseq uence of the breakdown of Migdal's theorem that certainly occurs in the cup rates due to their very low value of Fermi energy as compared to the charac teristic phonon energy. In order to numerically quantify the consequences o f the violation of the Migdal's approximation, we use the theoretical appro ach developed by Pietronero et al. [L. Pietronero, S. Strassler, C, Grimald i, Phys. Rev. B 52, 10516 (1995)] and Grimaldi et al. [C. Grimaldi, L. Piet ronero, S. Strassler, Phys. Rev. B 52, 10530 (1995)] on experimental data t aken from the literature. The effects on the electron-phonon coupling const ant lambda, on the critical temperature T-c and on the superconducting gap Delta are calculated also by means of a direct solution of the standard Eli ashberg equations and discussed in different kinds of superconducting mater ials both with low and high critical temperature. (C) 1999 Elsevier Science B.V. All rights reserved.