Abstract

The electron-phonon problem lies at the core of much of the understanding of “conventional” metals and superconductors. It was also long thought to be a theoretically solved problem. However, contrary to a widely accepted folk theorem, the Migdal approximation, upon which this understanding is based, breaks down when the dimensionless electron-phonon coupling is not small. I will discuss a variety of new features of this old problem that can be established theoretically using controlled quantum Monte-Carlo and strong-coupling expansions, and comment on their relevance to a variety of puzzling observations in otherwise conventional metals, especially the existence of a so-called “Plankian” bound on the T-linear resistivity and a corresponding rough bound on the magnitude of l determined from tunneling data in the superconducting stated. (This latter is particularly striking in light of decades of searches for more strongly coupled metals as part of the search for higher temperature superconductivity.)