Green function theory of dirty two-band superconductivity

TL;DR

This paper investigates how nonmagnetic impurities affect the superconducting transition temperature in a two-band superconductor, revealing the role of hybridization and odd-frequency pairs in impurity resilience.

Contribution

It provides a detailed theoretical analysis of impurity effects on two-band superconductivity, highlighting the influence of hybridization and phase on $T_c$ suppression.

Findings

Impurities decrease $T_c$ similarly in $s_{++}$ and $s_{+-}$ states.

Larger hybridization results in more moderate $T_c$ suppression.

Odd-frequency Cooper pairs generated by hybridization are broken by impurities.

Abstract

We study the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor, where we assume the equal-time spin-singlet s-wave pair potential in each conduction band and the hybridization between the two bands as well as the band asymmetry. In the clean limit, the phase of hybridization determines the stability of two states: called $s_{++}$ and $s_{+-}$. The interband impurity scatterings decrease $T_c$ of the two states exactly in the same manner when the Hamiltonian preserves time-reversal symmetry. We find that a superconductor with larger hybridization shows more moderate suppression of $T_c$. This effect can be explained by the presence of odd-frequency Cooper pairs which are generated by the band hybridization in the clean limit and are broken by impurities.