Subgap states in disordered superconductors

TL;DR

This paper develops a universal phenomenological model to describe the density of states in disordered superconductors, accounting for inhomogeneities and subgap states through a minimal set of parameters.

Contribution

It introduces a unified theory of optimal fluctuations that refines instanton approaches, linking microscopic disorder models to a universal phenomenological description.

Findings

Density of states characterized by broadening parameter Gamma and tail decay scale Gamma_tail.

Microscopic disorder models reduce to a universal random order parameter model.

Refined instanton methods for determining subgap state decay.

Abstract

We revise the problem of the density of states in disordered superconductors. Randomness of local sample characteristics translates to the quenched spatial inhomogeneity of the spectral gap, smearing the BCS coherence peak. We show that various microscopic models of potential and magnetic disorder can be reduced to a universal phenomenological random order parameter model, whereas the details of the microscopic description are encoded in the correlation function of the order parameter fluctuations. The resulting form of the density of states is generally described by two parameters: the width Gamma measuring the broadening of the BCS peak, and the energy scale Gamma_{tail} which controls the exponential decay of the density of the subgap states. We refine the existing instanton approaches for determination of Gamma_{tail} and show that they appear as limiting cases of a unified theory of optimal fluctuations in a nonlinear system. Application to various types of disorder is discussed.