Subgap states in disordered superconductors

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 Γ measuring the broadening of the BCS peak and the energy scale Γtail that controls the exponential decay of the density of subgap states. We refine the existing instanton approaches for determination of Γtail and show that they appear as limiting cases of a unified theory of optimal fluctuations in a nonlinear system. The application to various types of disorder is discussed.