Robustness of unconventional s-wave superconducting states against disorder

Unconventional superconductors are infamously unstable against the presence of nonmagnetic disorder, while the critical temperature of a conventional superconductor is insensitive to such disorder, as encapsulated in Anderson’s theorem. Generalization of Anderson’s theorem to superconductors with multiple bands has proven difficult. We investigate the robustness against disorder of superconductivity in systems with two bands. In multi-band systems, unconventional superconducting states are possible with momentum-independent (s-wave) pairing functions. We have developed a general framework, based on the self-consistent Born approximation, to understand the stability of orbitally non-trivial superconductors against disorder, and applied this framework to several multi-band superconductors. Unconventional s-wave states are found to be significantly more robust against disorder than analogous single-band states. Additionally, superconductors with momentum-dependent gaps inherit some robustness against disorder from the s-wave states with the same symmetry, in a significant deviation from the behavior exhibited in single-band superconductors.