Supercurrents through proximity layers. II. Numerical solution of superconducting-normal-superconducting and superconducting-superconducting-superconducting weak links

Abstract

There exist two distinctly different types of symmetric weak links. One contains a superconductor S/sub 1/, the other a normal metal N between the outside superconducting S regions, where the states S/sub 1/ and N refer to the properties of the isolated metals. Both types of weak links have multiple solutions of the pair potential for a fixed value of the dc current density. This multiplicity is theoretically elucidated. When the lengths of the S/sub 1/ and N regions, 2d/sub n/, are comparable to vertical-barxi/sub n/ vertical-bar or smaller, both types of weak links behave similarly. When 2d/sub n/ >> vertical-barxi/sub n/ vertical-bar, a superconducting-normal-superconducting (S-N-S) weak link behaves very much like a Josephson junction, but a superconducting-superconducting-superconducting (S-S/sub 1/-S) weak link behaves like a long superconducting wire with some of the Josephson-like properties remaining. Exact solutions of S-S/sub 1/-S and S-N-S weak links are calculated for different boundary conditions, lengths of the S/sub 1/ and N regions, and current densities. The latter are compared to previous analytical approximations.