Nonadiabatic pairing effects for tight-binding electrons interacting with phonons

TL;DR

This paper investigates how nonadiabatic electron-phonon interactions influence superconducting pairing in a 2D tight-binding model, revealing frequency and momentum dependence and enhancement with forward scattering, thus connecting theory to material properties.

Contribution

It provides a detailed analysis of nonadiabatic effects on superconducting pairing in a realistic 2D tight-binding model, extending previous simplified approaches.

Findings

Nonadiabatic effects induce strongly frequency and momentum dependent pairing.

Forward electron-phonon coupling significantly enhances pairing.

Results link nonadiabatic effects to specific material properties.

Abstract

The nonadiabatic electron-phonon corrections for the superconducting pairing are investigated for a specific tight-binding model corresponding to a 2d square lattice. This permits to investigate the role of various specific properties like the band filling, nesting effects and a realistic van Hove singularity on the superconducting effective pairing beyond Migdal's limit. The main results are: (i) Starting from a momentum independent electron-phonon coupling the nonadiabatic effects lead to an effective pairing which is strongly dependent on frequency and momentum. (ii) If instead the electron-phonon coupling is mainly forward (as due to correlation effects) the resulting pairing results to be strongly enhanced. These results confirm but also extend the simplified scheme used up to now to compute these properties. In this respect our results link the nonadiabatic effects to the specific properties of realistic materials.