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

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.

References in corpus (2)

• Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
• Optical absorption in the strong coupling limit of Eliashberg theory

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