Interference pattern of a long diffusive Josephson junction

TL;DR

This paper models how a magnetic field affects the critical current in a long, disordered Josephson junction, revealing a universal exponential decay of the interference pattern due to diffusive averaging.

Contribution

It provides a theoretical analysis of the magnetic field modulation of critical current in long diffusive Josephson junctions, showing a universal decay pattern independent of disorder strength.

Findings

Fraunhofer oscillations are smoothed out in long diffusive junctions.

The interference pattern exhibits an exponential decay at large magnetic fields.

The pattern's universality links to speckle correlations in optics.

Abstract

We calculate the modulation by a magnetic field of the critical current of a long disordered Josephson junction in the diffusive limit, i.e. when the dimensions of the junction are larger that the elastic mean free path, and when the length $L$ is much larger than the width $w$. Due to the averaging of the gauge invariant phase factor over diffusive trajectories, the well-known oscillations of the Fraunhofer pattern are smoothed out and replaced by an exponential decay at large field. The predicted pattern is universal, i.e., it is independent of the disorder strength. We point out an interesting relation with the physics of speckle correlations in optics of turbid media.