Strong coupling theory of impure superconductors : real space formalism

TL;DR

This paper develops a real space formalism to analyze how nonmagnetic impurities affect the transition temperature in superconductors within the electron-phonon model, revealing exponential suppression due to localization.

Contribution

It introduces a strong coupling theory using real space formalism to incorporate impurity effects into the superconducting transition temperature analysis.

Findings

Impurities cause exponential decrease in phonon-mediated interactions.

Derived Anderson's pairing condition from the Anomalous Green's function.

Localization effects significantly suppress superconductivity.

Abstract

In the electron-phonon model, the influence of nonmagnetic impurities on the transition temperature of superconductors is revisited. Anderson's pairing condition between time-reversed eigenstate pairs is derived from the physical constraint of the Anomalous Green's function. After this pairing condition is incorporated into the self-consistency equation, one may find that the phonon-mediated interaction decreases exponentially by localization.