Breakdown of Migdal's theorem and intensity of electron-phonon coupling in high-Tc superconductors

TL;DR

This paper investigates how the breakdown of Migdal's theorem affects electron-phonon coupling, critical temperature, and superconducting gap in high-Tc superconductors, suggesting strong electron-phonon interactions in materials like BSCCO.

Contribution

It quantifies the effects of Migdal's theorem breakdown on superconducting properties using theoretical and experimental data, highlighting significant deviations in high-Tc materials.

Findings

Large violation of Migdal's theorem increases e-p coupling in BSCCO.

In high-Tc superconductor BSCCO, e-p coupling and gap ratios indicate strong-coupling superconductivity.

No significant effects of Migdal's theorem breakdown are observed in low-Tc conventional superconductors.

Abstract

In this article we quantify the possible effects of the breakdown of Migdal's theorem on the electron-phonon (e-p) coupling constant, on the critical temperature and on the superconducting gap by examining different kinds of superconducting materials either with low and high critical temperature. We use the theoretical approach developed by Grimaldi, Pietronero and Strassler [PRB 52, 10516 & 10530 (1995)] on experimental data taken both from literature and from our recent break-junction tunneling experiments in Bi_2Sr_2CaCu_2O_{8+x} (BSCCO) [Physica C 275, 162 (1997) and cond-mat/9612220]. The results show that a large violation of the Migdal's theorem (as in BSCCO) yields to a large increase of the observed e-p coupling constant and, in a first approximation and by direct solution of the Eliashberg equations, to large but different increases of Tc and gap. The same theory gives no modifications when applied to low-Tc conventional superconductors. In BSCCO, the renormalized values of the e-p coupling constant and of the ratio 2Delta/kTc (1.85 and 4.98, respectively) are compatible with a strong-coupling electron-phonon origin of superconductivity.