Planar Josephson Tunnel Junctions in an Asymmetric Magnetic Field

TL;DR

This paper investigates how asymmetric magnetic fields affect the behavior of planar Josephson tunnel junctions, revealing unique diffraction patterns and potential applications in experiments and devices.

Contribution

It provides analytical and numerical analysis of asymmetric boundary conditions in Josephson junctions, highlighting novel diffraction patterns and static properties.

Findings

Asymmetric magnetic fields produce Fresnel-like diffraction patterns.

Numerical simulations explore behavior for various junction lengths.

Potential for new experiments and device applications.

Abstract

We analyze the consequences resulting from the asymmetric boundary conditions imposed by a non-uniform external magnetic field at the extremities of a planar Josephson tunnel junction and predict a number of testable signatures. When the junction length $L$ is smaller than its Josephson penetration depth $\lambda_j$, static analytical calculations lead to a Fresnel-like magnetic diffraction pattern, rather than a Fraunhofer-like one typical of a uniform field. Numerical simulations allow to investigate intermediate length ($L\approx \lambda_j$) and long ($L>\lambda_j$) junctions. We consider both uniform and $\delta$-shaped bias distributions. We also speculate on the possibility of exploiting the unique static properties of this system for basic experiments and devices.