Andreev states, supercurrents and interface effects in clean superconducting/normal metal multilayers

We present results for the local density of states in the superconducting (S) and normal metallic (N) layers of an SN multilayer, and the supercurrent, based on a Green function formalism, as an extension of previous calculations on NS, SNS and SNSNS systems. The gap function is determined self-consistently. Our systems are chosen to have a finite transverse width. We focus on phenomena which occur at so-called critical transverse widths, at which a new transverse mode is starting to contribute. It appears that for an arbitrary width the Andreev approximation (AA), which takes into account only Andreev reflection at the SN interfaces, works well. We show that at a critical width the AA breaks down. An exact treatment is required, which also considers ordinary reflections. In addition, we study the influence of an interface barrier on the coupling between the S layers.