Dirty two-band superconductivity with interband pairing order

TL;DR

This paper investigates how nonmagnetic impurities affect the superconducting transition temperature in a two-band superconductor with interband pairing, revealing that spin-triplet pairs are more sensitive to impurities than spin-singlet pairs.

Contribution

It provides a theoretical analysis of impurity effects on $T_c$ in two-band superconductors with interband s-wave pairing, highlighting the fragility of spin-triplet states.

Findings

Spin-singlet $T_c$ is insensitive to impurities.

Spin-triplet $T_c$ decreases with impurity concentration.

Odd-band-parity s-wave pairs are fragile under impurities.

Abstract

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, $T_c$ decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.