Critical temperature of an anisotropic superconductor containing both nonmagnetic and magnetic impurities

TL;DR

This paper derives a generalized formula for the critical temperature of anisotropic superconductors with both magnetic and nonmagnetic impurities, extending the Abrikosov-Gor'kov theory to complex pairing symmetries.

Contribution

It provides a comprehensive theoretical expression for the critical temperature considering arbitrary in-plane anisotropy and impurity effects in two-dimensional superconductors.

Findings

Derived a generalized critical temperature formula for anisotropic superconductors.

Extended Abrikosov-Gor'kov theory to include complex pairing symmetries.

Discussed implications for high-temperature superconductor impurities.

Abstract

The combined effect of both nonmagnetic and magnetic impurities on the superconducting transition temperature is studied theoretically within the BCS model. An expression for the critical temperature as a function of potential and spin-flip scattering rates is derived for a two-dimensional superconductor with arbitrary in-plane anisotropy of the superconducting order parameter, ranging from isotropic s-wave to d-wave (or any pairing state with nonzero angular momentum) and including anisotropic s-wave and mixed (d+s)-wave as particular cases. This expression generalizes the well-known Abrikosov-Gor'kov formula for the critical temperature of impure superconductors. The effect of defects and impurities in high temperature superconductors is discussed.