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

Andreev Bound States and Self-Consistent Gap Functions for SNS and SNSNS Systems

Andreev bound states in clean, ballistic SNS and SNSNS junctions are calculated exactly and by using the Andreev approximation (AA). The AA appears to break down for junctions with transverse dimensions chosen such that the motion in the longitudinal direction is very slow. The doubly degenerate states typical for the traveling waves found in the AA are replaced by two standing waves in the exact treatment and the degeneracy is lifted. A multiple-scattering Green's function formalism is used, from which the states are found through the local density of states. The scattering by the interfaces in any layered system of ballistic normal metals and clean superconducting materials is taken into account exactly. The formalism allows, in addition, for a self-consistent determination of the gap function. In the numerical calculations the pairing coupling constant for aluminum is used. Various features of the proximity effect are shown

Size-effects in the Density of States in NS and SNS junctions

The quasiparticle local density of states (LDOS) is studied in clean NS and SNS junctions with increasing transverse size, from quasi-one-dimensional to three-dimensional. It is shown that finite transverse dimensions are related to pronounced effects in the LDOS, such as fast oscillations superimposed on the quasiparticle interference oscillations (for NS) and additional peaks in the bound state spectrum in the subgap region (for SNS). Also, the validity of the Andreev approximation is discussed. It turns out to be an acceptable approximation in all situations tested.Comment: 9 pages, RevTex, 5 figures, accepted in Phys. Rev.