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## 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.