Strong Coupling Theory of Superconductivity

TL;DR

This paper discusses the microscopic foundations and quasiclassical transport equations of strong-coupling superconductors, emphasizing their equilibrium and non-equilibrium properties, and calculates their dynamical conductivity.

Contribution

It formulates the basic equations for strong-coupling superconductors based on Fermi-liquid and Migdal-Eliashberg theories, providing a framework for analyzing their transport properties.

Findings

Derived the linear response theory for strong-coupling superconductors.

Calculated the dynamical conductivity in the strong-coupling regime.

Presented a microscopic foundation for the phenomenological Fermi-liquid model.

Abstract

The electronic properties of correlated metals with a strong electron-phonon coupling may be understood in terms of a combination of Landau's Fermi-liquid theory and the strong-coupling theory of Migdal and Eliashberg. In these lecture notes we discuss the microscopic foundations of this phenomenological Fermi-liquid model of correlated, strong-coupling metals. We formulate the basic equations of the model, which are quasiclassical transport equations that describe both equilibrium and non-equilibrium phenomena for the normal and superconducting states of a metal. Our emphasis is on superconductors close to equilibrium, for which we derive the general linear response theory. As an application we calculate the dynamical conductivity of strong-coupling superconductors.