Corbino-geometry Josephson weak links in thin superconducting films

TL;DR

This paper analyzes a Corbino-geometry Josephson weak link in thin superconducting films, deriving exact solutions and studying dynamics, resistance, and vortex effects, providing insights different from traditional sandwich-type junctions.

Contribution

It introduces an integral equation approach for phase difference in Corbino geometries and derives exact solutions for vortex configurations and dynamic properties.

Findings

Exact solutions for phase difference with N vortices at zero current

Derived effective resistance and viscous drag coefficient

Calculated critical current with nearby Pearl vortex

Abstract

I consider a Corbino-geometry SNS (superconducting-normal-superconducting) Josephson weak link in a thin superconducting film, in which current enters at the origin, flows outward, passes through an annular Josephson weak link, and leaves radially. In contrast to sandwich-type annular Josephson junctions, in which the gauge-invariant phase difference obeys the sine-Gordon equation, here the gauge-invariant phase difference obeys an integral equation. I present exact solutions for the gauge-invariant phase difference across the weak link when it contains an integral number N of Josephson vortices and the current is zero. I then study the dynamics when a current is applied, and I derive the effective resistance and the viscous drag coefficient; I compare these results with those in sandwich-type junctions. I also calculate the critical current when there is no Josephson vortex in the weak link but there is a Pearl vortex nearby.