Spectral features of the proximity effect

We calculate the local density of states (LDOS) of a superconductor-normal metal sandwich at arbitrary impurity concentration. The presence of the sup erconductor induces a gap in the normal metal spectrum that is proportional to the inverse of the elastic mean free path I for rather clean systems. F or a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to I that approaches the behavior predicted b y the Usadel equation (diffusive limit). (C) 2000 Elsevier Science B.V. All rights reserved.