A Vertex Correction in the Gap Equation for the High Temperature Superconductors

TL;DR

This paper demonstrates that vertex corrections are crucial in the gap equation for high-temperature superconductors, leading to a significant enhancement of the critical temperature despite strong inelastic scattering effects.

Contribution

It introduces a vertex correction based on the generalized Ward identity into the gap equation for high Tc cuprates, challenging the validity of Migdal's theorem in this context.

Findings

Vertex correction enhances Tc despite strong pair breaking.

Violation of Migdal theorem in high Tc cuprates.

Strong inelastic scattering observed in experiments is incorporated.

Abstract

We show that the Migdal theorem is obviously violated in the high Tc cuprates and the vertex correction should be included, in particular, in the gap equation, in order to be consistent with the anomalously strong inelastic scattering in the ``hot spots'', which is observed from the various normal state experiments. The vertex correction is obtained by utilizing the generalized Ward identity, which is shown to hold in the important scattering channel for the pairing interaction in the high Tc cuprates. As a result, we find a strong enhancement of Tc from the vertex correction despite of the strong pair breaking effect due to the inelastic scattering.