Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity

TL;DR

This paper extends the Abrikosov-Gor'kov theory to multiband superconductors with impurities, analyzing how impurities affect critical temperature and gap renormalization across various anisotropic and sign-reversal scenarios.

Contribution

It provides a generalized analytical framework for impurity effects in multiband superconductors, including cases with arbitrary interband anisotropy and sign reversal.

Findings

Analytical solutions for critical temperature suppression in limiting cases

Numerical results for two-band models showing impurity effects

Renormalization of superconducting gap at all temperatures

Abstract

We generalize Abrikosov-Gor'kov solution of the problem of weakly coupled superconductor with impurities on the case of a multiband superconductor with arbitrary interband order parameter anisotropy, including interband sign reversal of the order parameter. The solution is given in terms of the effective (renormalized) coupling matrix and describes not only $T_c$ suppression but also renormalization of the superconducting gap basically at all temperatures. In many limiting cases we find analytical solutions for the critical temperature suppression. We illustrate our results by numerical calculations for two-band model systems.