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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.