The Effects of the Breakdown of Migdal's Theorem in Various Superconductors

Abstract

In this work we investigate some effects of the breakdown of Migdal's theorem in high and low-Tc superconductors. In the cuprates the electronic bandwidth has a very low value compared to the characteristic phonon energy and, in order to reproduce the experimental Tc and tunneling data in the framework of the Eliashberg theory for strong electron-boson interaction it is necessary to use large values of the coupling constant. Our purpose is to numerically quantify the correlation between the amount of violation of the Migdal's theorem and the renormalization of the coupling constant λ, of the gap Δ and of Tc by examining different kinds of superconducting materials. For this task we use the theoretical approach developed by Grimaldi, Pietronero and Strässler [PRB 52, 10516 & 10530, 1995], together with the real-axis direct solution of the Eliahsberg equations in s -wave pair symmetry.