SUPER-CURRENTS THROUGH PROXIMITY LAYERS .2. NUMERICAL-SOLUTION OF SUPERCONDUCTING-NORMAL-SUPERCONDUCTING AND SUPERCONDUCTING-SUPERCONDUCTING-SUPERCONDUCTING WEAK LINKS

There exist two distinctly different types of symmetric weak links. One contains a superconductor S1, and the other contains a normal metal N between the outside superconducting S regions, where the states S1 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 S1 and N regions, 2dn, are comparable to |ξn| or smaller, both types of weak links behave similarly. When 2dn|ξn|, a superconducting-normal-superconducting (SNS) weak link behaves very much like a Josephson junction, but a superconducting-superconducting-superconducting (S-S1-S) weak links behaves like a long superconducting wire with some of the Josephson-like properties remaining. Exact solutions of S-S1-S and S-N-S weak links are calculated for different boundary conditions, lengths of the S1 and N regions, and current densities. The latter are compared to previous analytical approximations. © 1979 The American Physical Society.