Confocal Annular Josephson Tunnel Junctions

TL;DR

This paper develops a comprehensive theory for confocal annular Josephson tunnel junctions, revealing how their geometry influences fluxon behavior, static solutions, and electromagnetic radiation, with implications for device design.

Contribution

It introduces a new theoretical framework for confocal annular Josephson junctions, including derivation of threshold curves and motion equations considering non-uniform widths.

Findings

Threshold curves derived for short junctions with trapped vortices

Fluxon dynamics affected by non-uniform annulus width

Electromagnetic radiation concentrated at ellipse points

Abstract

The physics of Josephson tunnel junctions drastically depends on their geometrical configurations and here we show that also tiny geometrical details play a determinant role. More specifically, we develop the theory of short and long confocal annular Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. The behavior of a circular annular Josephson tunnel junction is then seen to be simply a special case of the above result. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with trapped Josephson vortices. For longer junctions a numerical analysis is carried out after the derivation of the appropriate motion equation for the Josephson phase. We found that the system is modeled by a modified and perturbed sine-Gordon equation with a space dependent effective Josephson penetration length inversely proportional to the local junction width. Both the fluxon statics and dynamics are deeply affected by the non-uniform annulus width. Static zero-field multiple-fluxon solutions exist even in presence of a large bias current. The tangential velocity of a traveling fluxon is not determined by the balance between the driving and drag forces due to the dissipative losses. Furthermore, the fluxon motion is characterized by a strong radial inward acceleration which causes electromagnetic radiation concentrated at the ellipse equatorial points.