Journal
PHYSICAL REVIEW B
Volume 68, Issue 16, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevB.68.165102
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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.
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