Model calculations of the proximity effect in finite multilayers

The proximity-effect theory developed by Takahashi and Tachiki for infinite multilayers is applied to multilayer systems with a finite number of layers in the growth direction. The purpose is to investigate why previous applications to infinite multilayers fail to describe the measured data satisfactorily. Surface superconductivity may appear, depending on the thickness of the covering normal metallic N layers on both the top and the bottom. The parameters used are characteristic for V/Ag and Nb/Pd systems. The nucleation process is studied as a function of the system parameters.Comment: 12 pages, 15 figures, RevTe

The influence of the boundary resistivity on the proximity effect

We apply the theory of Takahashi and Tachiki in order to explain theoretically the dependence of the upper critical magnetic field of a S/N multilayer on the temperature. This problem has been already investigated in the literature, but with a use of an unphysical scaling parameter for the coherence length. We show explicitely that, in order to describe the data, such an unphysical parameter is unnecessary if one takes into account the boundary resisitivity of the S/N interface. We obtain a very good agreement with the experiments for the multilayer systems Nb/Cu and V/Ag, with various layer thicknesses.Comment: 12 pages, 5 figure

Andreev States in long shallow SNS constrictions

We study Andreev bound states in a long shallow normal constriction, which is open to a superconductor at both ends. The interesting features of such setup include the absence of electron-hole symmetry and the interference of electron waves along the constriction. We compare results of a numerical approach based on the Bogoliubov equations with those of a refined semiclassical description. Three types of Andreev bound states occur in the constriction: {\it i}) one where both electron and hole wave part of the bound state propagate through the constriction, {\it ii}) one where neither electron nor hole wave part propagate, and {\it iii}) one where only the electron wave propagates. We show that in a wide energy region the spacing between the Andreev states is strongly modulated by the interference of electron waves passing the constriction

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.

Calcualtion of the upper critical fields in Nb/Ta multilayers.

The Takahashi-Tachiki proximity-effect theory is applied to the Nb/Ta multilayer system. The diffusion coefficients of the two metals and the critical temperature of Nb are used as free parameters in fitting experimental phase diagrams. Magnetic-coherence-length scaling is used in order to obtain phase diagrams that best reproduce the measured data. Several parameter sets can compete in fitting an experimental curve. It is not always possible to decide which set gives the most realistic result