The effects of the breakdown of Migdal's theorem in various superconductors

In this work we investigate some effects of the breakdown of Migdal's theor em in high and low-T-c superconductors. In the cuprates the electronic band width has avery low value compared to the characteristic phonon energy and, in order to reproduce the experimental T-c and tunneling data in the frame work of the Eliashberg theory for strong electron-boson interaction it is n ecessary to use large values of the coupling constant. Our purpose is to nu merically quantify the correlation between the amount of violation of the M igdal's theorem and the renormalization of the coupling constant lambda, of the gap Delta and of T-c by examining different kinds of superconducting m aterials. For this task we use the theoretical approach developed by Grimal di, Pietronero and Strassler [PRB 52, 10516 & 10530, 1995], together with t he real-axis direct solution of the Eliahsberg equations in s-wave pair sym metry.