Josephson junctions in thin and narrow rectangular superconducting strips

TL;DR

This paper analyzes how a Josephson junction's critical current varies with magnetic field in a thin, narrow superconducting strip, providing detailed phase difference calculations.

Contribution

It introduces a detailed model for the phase difference and critical current dependence in Josephson junctions within narrow superconducting strips.

Findings

Calculated the spatial phase difference across the junction.

Derived the magnetic field dependence of the critical current.

Provided analytical expressions for the critical current variation.

Abstract

I consider a Josephson junction crossing the middle of a thin rectangular superconducting strip of length L and width W subjected to a perpendicular magnetic induction B. I calculate the spatial dependence of the gauge-invariant phase difference across the junction and the resulting B dependence of the critical current Ic(B).