Elliptic Annular Josephson Tunnel Junctions in an external magnetic field: The statics

TL;DR

This paper studies the static properties of elliptic annular Josephson junctions under external magnetic fields, analyzing critical current behavior, phase profiles, and effects of eccentricity through theoretical, numerical, and experimental approaches.

Contribution

It provides a comprehensive analysis of elliptic annular Josephson junctions, including derivation of threshold curves, phase profiles, and experimental validation, extending known results to more general elliptic geometries.

Findings

Critical current dependence on magnetic field and eccentricity.

Existence of multiple phase profiles with fluxon-antifluxon pairs.

Transverse magnetic field effects equivalent to in-plane fields in symmetric samples.

Abstract

We have investigated the static properties of one-dimensional planar Josephson tunnel junctions in the most general case of elliptic annuli. We have analyzed the dependence of the critical current in the presence of an external magnetic field applied either in the junction plane or in the perpendicular direction. We report a detailed study of both short and long elliptic annular junctions having different eccentricities. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with one trapped Josephson vortex. For longer junctions a numerical analysis is carried out after the derivation of the appropriate Perturbed sine-Gordon Equation. For a given applied field we find that a number of different phase profiles exist which differ according to the number of fluxon-antifluxon pairs. We demonstrate that in samples made by specularly symmetric electrodes a transverse magnetic field is equivalent to an in-plane field applied in the direction of the current flow. Varying the ellipse eccentricity we reproduce all known results for linear and ring-shaped Josephson tunnel junctions. Experimental data on high-quality Nb/Al-AlOx/Nb elliptic annular junctions support the theoretical analysis provided self-field effects are taken into account.