Andreev states, supercurrents and interface effects in clean SN   multilayers
  We present results for the local density of states in the S and N layers of a SN multilayer, and the supercurrent, based on a Green's function formalism, as an extension of previous calculations on NS, SNS and SNSNS systems. The gap function is determined selfconsistently. 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 considers also ordinary reflections. In addition, we study the influence of an interface barrier on the coupling between the S-layers. 
C. Ciuhu, A. Lodder, R.E.S Rotadoy, R.T.W. Koperdraad