Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0-kappa-junctions

TL;DR

This paper theoretically analyzes the eigenmodes and stability of fractional vortices in long Josephson junctions with phase discontinuities, revealing stable configurations, eigenfrequency behaviors, and vortex molecule formation.

Contribution

It provides a detailed theoretical study of eigenmodes and stability of fractional vortices in long Josephson junctions with arbitrary phase discontinuities, including numerical calculations and vortex molecule behavior.

Findings

Only two of four vortex configurations are stable.

Single vortices have oscillatory eigenmodes within the plasma gap.

Vortex splitting and vortex molecule formation depend on the distance between vortices.

Abstract

We investigate theoretically the eigenmodes and the stability of one and two arbitrary fractional vortices pinned at one and two $\kappa$-phase discontinuities in a long Josephson junction. In the particular case of a single $\kappa$-discontinuity, a vortex is spontaneously created and pinned at the boundary between the 0 and $\kappa$-regions. In this work we show that only two of four possible vortices are stable. A single vortex has an oscillatory eigenmode with a frequency within the plasma gap. We calculate this eigenfrequency as a function of the fractional flux carried by a vortex. For the case of two vortices, pinned at two $\kappa$-discontinuities situated at some distance $a$ from each other, splitting of the eigenfrequencies occur. We calculate this splitting numerically as a function of $a$ for different possible ground states. We also discuss the presence of a critical distance below which two antiferromagnetically ordered vortices form a strongly coupled ``vortex molecule'' that behaves as a single object and has only one eigenmode.