Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations

We study the tails of the density of states (DOS) in a diffusive superconductor-normal metal-superconductor (SNS) junction below the Thouless gap. We show that long-wave fluctuations of the concentration of impurities in the normal layer lead to the formation of subgap quasiparticle states, and calculate the associated subgap DOS in all effective dimensionalities. We compare the resulting tails with those arising from mesoscopic gap fluctuations, and determine the dimensionless parameters controlling which contribution dominates the subgap DOS. We observe that the two contributions are formally related to each other by a dimensional reduction.