Interplay of Anderson localization and proximity effect
We study proximity effect in a disordered normal metallic wire attached to a bulk superconductor. Standard approach to this problem is based on the quasiclassical Usadel equation, which neglects localization effects. In this work we employ the fully quantum approach of nonlinear sigma model and find an exact expression for the global (spatially integrated) density of states applicable at all energies. In the vicinity of the Fermi level, localization corrections are dominant and considerably modify the quasiclassical result. In this limit we also calculate local (spatially resolved) density of states fully taking into account quantum interference effects.