Density of States in a Mesoscopic SNS Junction

The semiclassical theory of proximity effects predicts a gap E_g∼ℏD/L² in the excitation spectrum of a long diffusive superconductor/normal-metal/superconductor (SNS) junction. Mesoscopic fluctuations lead to anomalously localized states in the normal part of the junction.As a result, a nonzero, yet exponentially small, density of states (DOS) appears at energies below E_g. In the framework of the supermatrix nonlinear σ model, these prelocalized states are due to the instanton configurations with broken supersymmetry. The exact result for the DOS near the semiclassical threshold is found, provided the dimensionless conductance of the normal part G_N is large. The case of poorly transparent interfaces between the normal and superconductive regions is also considered. In this limit, the total number of subgap states may be large.