Vortex structure in exponentially shaped Josephson junctions

TL;DR

This paper presents numerical analysis of vortex structures and stability in exponentially shaped long Josephson junctions, revealing how geometry influences magnetic flux and matching experimental critical curves.

Contribution

It introduces a detailed numerical study of vortex stability in exponentially shaped Josephson junctions, including the effects of geometry and shape parameters.

Findings

Renormalization of magnetic flux due to junction shape

Comparison of vortex structures in different geometries

Numerical critical curves align with experimental data

Abstract

We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Each solution of the corresponding boundary value problem is associated with the Sturm-Liouville problem whose minimal eigenvalue allows to make a conclusion about the stability of the vortex. The change in width of the junction leads to the renormalization of the magnetic flux in comparison to the case of a linear one-dimensional model. We study the influence of the model's parameters and, particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.