Fractional vortex in asymmetric 0-$\pi$ long Josephson junctions

TL;DR

This paper studies asymmetric 0-$\pi$ Josephson junctions, revealing the properties of fractional vortices, including their depinning currents and flux variations under bias, highlighting their asymmetric and dynamic nature.

Contribution

It introduces the analysis of fractional vortices in asymmetric 0-$\pi$ Josephson junctions, focusing on their depinning currents and flux changes, which was not previously detailed.

Findings

Depinning current differs for positive and negative bias.

Fractional flux varies with applied bias.

Asymmetric tails decay on different length scales.

Abstract

We consider an infinitely long 0-$\pi$ Josephson junction consisting of 0 and $\pi$ regions having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. The ground state of such a junction corresponds to a spontaneosly formed asymmetric semifluxon with tails decaying on different length scales. We calculate the depinning current of such a fractional vortex and show that it is different for positive and negative bias polarity. We also show that upon application of a bias current, the fractional flux (topological charge) associated with the vortex changes. We calculate the range of fractional flux associated with the vortex when the bias changes from negative to positive critical (depinning) values.