Семинар международной лаборатории физики конденсированного состояния: Pavel Ostrovsky, (MPI Stuttgart, Germany) "Interplay between Anderson localization and proximity effect"
When a normal metal is connected to a superconductor, Cooper pairs penetrate in the normal region and induce superconducting correlations there. This phenomenon is known as the proximity effect. Its main manifestation is a suppression of the local density of states in the normal part of the junction. Standard description of the proximity effect is based on the quasiclassical Usadel equation, which neglects possible electron interference. The latter is responsible for Anderson localization in the disordered metal and in general competes with the proximity effect reducing the superconducting correlations. In this work we develop a fully quantum approach based on the nonlinear sigma model to describe both proximity effect and localization within the same framework. We obtain exact results for the global (spatially integrated) density of states in the normal part of the junction applicable at all energies. At low energies, interference effects are strongest and considerably modify the quasiclassical result. In this limit we also calculate local (spatially resolved) density of states. We find that localization limits the spatial extent of the proximity effect but at the same time, and quite counterintuitively, enhances it at short distances.