Superelliptic Josephson Tunnel Junctions

TL;DR

This paper investigates the magnetic diffraction patterns of superelliptic Josephson tunnel junctions, deriving explicit formulas and analyzing how their shape influences the decay of sidelobes in their magnetic response.

Contribution

It introduces a detailed analysis of superelliptic junction shapes and derives explicit expressions for their magnetic diffraction patterns, expanding understanding of shape effects on Josephson junction behavior.

Findings

Derived explicit threshold curves for superelliptic junctions

Analyzed the decay rate of sidelobes in magnetic patterns

Showed shape influences magnetic diffraction characteristics

Abstract

The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study is made of their magnetic patterns with emphasis on the rate of decay of the sidelobes amplitudes for large field amplitudes.