Beyond the effective length: How to analyze magnetic interference patterns of thin-film planar Josephson junctions with finite lateral dimensions

TL;DR

This paper develops a simulation-based method to analyze magnetic interference patterns in thin-film planar Josephson junctions with finite size, accounting for non-local electrodynamics, to accurately extract junction parameters.

Contribution

It extends Clem's technique to various geometries and verifies the geometry dependence of interference pattern periodicity experimentally.

Findings

Periodic interference pattern limits are geometry independent for extreme aspect ratios.

Experimental verification of the $L/W$ dependence of the magnetic field periodicity.

Fourier analysis enables accurate extraction of critical current distribution.

Abstract

The magnetic field dependent critical current $I_{\text{c}}(B)$ of a Josephson junction is determined by the screening currents in its electrodes. In macroscopic junctions, a local vector potential drives the currents, however, in thin film planar junctions, with electrodes of finite size and various shapes, they are governed by non-local electrodynamics. This complicates the extraction of parameters such as the geometry of the effective junction area, the effective junction length and, the critical current density distribution from the $I_{\text{c}}(B)$ interference patterns. Here we provide a method to tackle this problem by simulating the phase differences that drive the shielding currents and use those to find $I_{\text{c}}(B)$. To this end, we extend the technique proposed by John Clem [Phys. Rev. B, \textbf{81}, 144515 (2010)] to find $I_{\text{c}}(B)$ for Josephson junctions separating a superconducting strip of length $L$ and width $W$ with rectangular, ellipsoid and rhomboid geometries. We find the periodicity of the interference pattern ($\Delta B$) to have geometry independent limits for $L \gg W$ and $L \ll W$. By fabricating elliptically shaped S$-$N$-$S junctions with various aspect ratios, we experimentally verify the $L/W$ dependence of $\Delta B$. Finally, we incorporate these results to correctly extract the distribution of critical currents in the junction by the Fourier analysis of $I_{\text{c}}(B)$, which makes these results essential for the correct analysis of topological channels in thin film planar Josephson junctions.