Effect of Coulomb Interaction and Disorder on Density of States in Conventional Superconductors

TL;DR

This paper calculates how Coulomb interactions and disorder affect the density of states in conventional superconductors, revealing a unique energy dependence and the interplay between Coulomb effects and superconducting fluctuations.

Contribution

It provides a perturbative analysis of the density of states considering Coulomb interactions and disorder, highlighting their coupled effects in the superconducting state.

Findings

Correction exhibits a dip at twice the superconducting gap energy.

Energy dependence of the correction differs from the normal state.

No divergence occurs at the gap edge, validating the perturbative approach.

Abstract

The density of states of the disordered s-wave superconductor is calculated perturbatively. The effect of Coulomb interaction on diffusively moving electrons in the normal state has been known before, but in the superconducting state both diffuson and the screened Coulomb interaction are modified. Therefore, the correction to the density of states in the superconducting state exhibits an energy dependence different from that of the normal state. There is a dip structure in the correction part because the interaction has a peak at twice the energy of the superconducting gap. The Coulomb interaction and the superconducting fluctuation cannot be treated separately because the density fluctuation is coupled to the phase fluctuation in the superconducting state. This coupling results in the absence of divergence around the gap edge in the correction part, which suggests the validity of this perturbation calculation.