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

V Bosboom,M Yu Kupriyanov,A A Golubov,J J W Van Der Vegt

doi:10.1088/1361-6668/ac2d79

Abstract

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.

Highlights

One of the important problems in the development of superconducting electronics is the design of Josephson junctions, which are nonlinear elements of superconducting circuits
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)
We studied the behavior of the current density and density of states (DOS) in the SN-N-NS junction

Summary

Introduction

One of the important problems in the development of superconducting electronics is the design of Josephson junctions, which are nonlinear elements of superconducting circuits. We can assume that all materials satisfy the dirty limit condition lj ≪ ξj, where j = N, S denotes either the normal metal strip or the superconducting electrode, lj is the mean free path and ξj the superconducting coherence length. We assume that the width W of the junction is much smaller than the Josephson penetration depth λJ so that magnetic effects inside the junction can be neglected Under these assumptions the junction can be described in the framework of the two-dimensional Usadel equations [8], which have the form: Here Gj is the 2×2 matrix Usadel Green’s function in layer j, i is the imaginary unit, and τ3 and ∆ˆ are the third Pauli matrix and the pair potential matrix respectively:.

Stationary equations

Current density

Density of states

Discussion and conclusion