Selfconsistent 3D model of SN-N-NS Josephson junctions

We develop a quantitative model describing the distribution of the supercurrent density and density of states in SN-N-NS type Josephson junctions in three dimensions (S is a superconductor and N is a normal metal). The model is based on the self-consistent solution of the quasiclassical Usadel equations using the finite element method. We investigate the influence of the proximity effect on the properties of the junction as a function of phase difference across the structure for various spatial dimensions and material parameters of S, N metals. The results are consistent with analytical solutions in the thin N layer limit and show consistent behavior for a large range of junction parameters. The results may serve to design nanoscale Josephson junctions for use in superconducting digital circuits.