Bound states and impurity averaging in unconventional superconductors

TL;DR

This paper investigates impurity states in unconventional superconductors, showing they are broad resonances rather than true bound states, which challenges assumptions in impurity averaging theories and highlights limitations of the non-crossing approximation.

Contribution

It demonstrates that impurity states are broad resonances with anisotropic wavefunctions, not true bound states, and questions the validity of the non-crossing approximation in 2D systems.

Findings

Impurity states are broad resonances, not midgap bound states.

Impurity resonances do not cause anomalous hopping.

Non-crossing approximation fails in strictly 2D systems.

Abstract

The question of anomalous transport due to a band of impurity states in unconventional superconductors is discussed. In general, the bound state energies are not in midgap, even in the unitarity limit. This implies that, generically, the states associated with impurities are broad resonances, not true bound states. There is no impurity band in the usual sense of the phrase. The wavefunctions of these resonances possess interesting anisotropies in real space, but this does not result in anomalous hopping between impurities. I conclude that the system of resonances produces no qualitative modifications to the T-matrix theory with impurity averaging which is normally used to treat the low-temperature transport of unconventional superconductors. However, users of this method often assume a density of states which is symmetric around the chemical potential. This is not normally the case. It is found that the non-crossing approximation is not valid in a strictly two-dimensional system.