Current-phase relation in an intermediately coupled superconductor-superconductor junction

The limiting configuration of the S-N-S{'} junction in which the N-layer thickness is of the order of the screening length in metals ({}1--2 {}) may serve as a model for a clean S-S{'} interface. This configuration supports one N-layer-attached gap state (manifold), with eigenenergy close to and less than the smaller superconducting gap. This gap state is interpreted as the excitation associated with breakage of interface-attached Cooper pairs, comprised of one electron from each side of the thin-N layer. The corresponding junction's current-phase ({ψ}) relation is calculated. The gap state is shown to contribute an appreciable ``sin(2{ψ})'' correction term to the ``sin({ψ})'' Josephson term. The corresponding maximum-current magnetic-flux dependence of a two-junction configuration (SQUID) is predicted to have zeros shifted from their common loci at half-integer flux quanta.