Local-phonon model of strong electron-phonon interactions inA15compounds and other strong-coupling superconductors

We propose a model in which a single atom interacts strongly with a Fermi gas of spinless electrons. We find that the electrons provide an effective double-well potential for the atom. The electron-phonon coupling $\Lambda$ is renormalized downward with decreasing temperature, provided that $\Lambda$ is large at high temperatures. The model is consistent with the experimental temperature dependence of the Pauli susceptibility and the resistivity as well as with the violation of Mattheissen's rule. It provides a possible explanation for why the observed martensitic transition is so small. We find that the violation of Migdal's theorem implies time-retarded interactions between hops of the atom from one minimum of the double well to the other.