Ground states of one and two fractional vortices in long Josephson 0-kappa-junctions

TL;DR

This paper investigates the properties, stability, and ground states of fractional vortices in long Josephson junctions with arbitrary phase discontinuities, revealing how their configurations depend on the separation distance between discontinuities.

Contribution

It provides a theoretical analysis of fractional vortices at arbitrary phase discontinuities, including stability, ground state configurations, and the influence of discontinuity separation.

Findings

Two stable ground states are not mirror symmetric.

Ground states depend strongly on the distance between discontinuities.

A crossover distance exists where ground state characteristics change.

Abstract

Half integer Josephson vortices in 0-$\pi$-junctions, discussed theoretically and observed experimentally, spontaneously appear at the point where the Josephson phase is $\pi$-discontinuous. The creation of \emph{arbitrary} discontinuities of the Josephson phase has been demonstrated recently. Here we study fractional vortices formed at an arbitrary $\kappa$-discontinuity, discuss their stability and possible ground states. The two stable states are not mirror symmetric. Furthermore, the possible ground states formed at two $\kappa$-discontinuities separated by a distance $a$ are investigated, and the energy and the regions of stability of each ground state are calculated. We also show that the ground states may strongly depend on the distance $a$ between the discontinuities. There is a crossover distance $a_c$ such that for $a<a_c$ and for $a>a_c$ the ground states may be qualitatively different.