Comment on "Theory of Impure Superconductors: Anderson versus Abrikosov and Gor'kov"

TL;DR

This paper defends the Abrikosov-Gor'kov theory of impure superconductors against recent criticisms, demonstrating its validity for realistic retarded interactions and confirming its accuracy through numerical calculations.

Contribution

It clarifies that the Abrikosov-Gor'kov formalism remains valid for retarded interactions, countering recent alternative approaches based on Green's functions not derived from Dyson equations.

Findings

Numerical results support the validity of Abrikosov-Gor'kov theory for retarded interactions.

Corrections proposed by Kim and Overhauser are not applicable to realistic interactions.

The traditional theory accurately predicts impurity effects on superconducting transition temperature.

Abstract

In a recent article, Kim and Overhauser [Phys. Rev. B 47, 8025 (1993)] have found fault with the theory of impure superconductors by Abrikosov and Gor'kov and have proposed an alternative formalism based on Green's functions which are not derivable from a Dyson equation. Although the corrections to the Abrikosov-Gor'kov theory found by Kim and Overhauser are correct for non-retarded interactions, I argue that these corrections do not appear when one treats realistic retarded interactions within the field-theoretic approach of Abrikosov and Gor'kov. Direct numerical computation of the impurity-induced suppression of the superconducting transition temperature Tc for both retarded and non-retarded interactions illustrates these points. I conclude that Abrikosov-Gor'kov theory applied to physical electron-electron interactions yields a tractable formalism which accurately predicts the effects of magnetic and non-magnetic impurities on Tc.