Self-Consistent Modification To The Electron Density Of States Due To Electron-Phonon Coupling In Metals

TL;DR

This paper investigates the self-consistency of the Migdal approximation in metals with strong electron-phonon coupling, revealing that significant changes in the electron density of states occur only at very high coupling levels without a clear crossover point.

Contribution

It provides a detailed analysis of the limits of the Migdal approximation and how electron-phonon interactions affect the electron density of states in metals.

Findings

Significant density of states modifications occur only at very high coupling strengths.

No critical coupling value or crossover regime invalidates the Migdal approximation.

The phonon spectrum characteristics strongly influence electron band collapse.

Abstract

The "standard" theory of a normal metal consists of an effective electron band which interacts with phonons and impurities. The effects due to the electron-phonon interaction are often delineated within the Migdal approximation; the properties of many simple metals are reasonably well described with such a description. On the other hand, if the electron-phonon interaction is sufficiently strong, a polaron approach is more appropriate. The purpose of this paper is to examine to what degree the Migdal approximation is self-consistent, as the coupling strength increases. We find that changes in the electron density of states become significant for very large values of the coupling strength; however, there is no critical value, nor even a crossover regime where the Migdal approximation has become inconsistent. Moreover, the extent to which the electron band collapses is strongly dependent on the detailed characteristics of the phonon spectrum.