Validity of Anderson's theorem for s-wave superconductors

TL;DR

This study examines the validity of Anderson's theorem in disordered s-wave superconductors, revealing that the critical temperature is highly sensitive to impurity concentration and potential strength, thus violating the theorem under strong scattering conditions.

Contribution

It provides a detailed analysis of Anderson's theorem applicability in disordered superconductors using the CPA method, highlighting conditions where the theorem fails.

Findings

$T_{c}$ is sensitive to impurity concentration and potential strength.

Anderson's theorem holds only at low impurity concentrations and weak potentials.

Strong scattering leads to suppression of $T_{c}$, violating the theorem.

Abstract

We investigate validity of Anderson's theorem (AT) for disordered s-wave superconductors in a negative U Hubbard model with random on-site energies, $\epsilon_{i}$. The superconducting critical temperature, $T_{c}$, is calculated in the coherent potential approximation (CPA) as a function of impurity concentration, $c$, the random potentials for different band filling. In contradiction to Anderson's theorem, we found that $T_{c}$ is dramatically sensitive with respect to $c$ and $\epsilon_{i}$. Our results shows that for low impurity concentrations and weak on-site energies, $\epsilon_{i}$, the AT is valid, while in the strong scattering limit even for low impurity concentration, $T_{c}$ is very small with respect to the clean system and by increasing $c$ it is completely suppressed, hence AT is violated in this regime.