Dynamics and stability of vortex-antivortex fronts in type II superconductors

TL;DR

This paper analyzes the stability of vortex-antivortex fronts in type II superconductors, showing that fast-moving fronts are stable without temperature coupling, which advances understanding of vortex pattern formation.

Contribution

It introduces a linear stability analysis for vortex-antivortex fronts, revealing stability conditions that differ from previous approximate stationary models.

Findings

Fast vortex fronts are stable without temperature coupling.

In-plane anisotropy does not induce instability at high velocities.

Method provides a foundation for analyzing more complex vortex dynamics.

Abstract

The dynamics of vortices in type II superconductors exhibit a variety of patterns whose origin is poorly understood. This is partly due to the nonlinearity of the vortex mobility which gives rise to singular behavior in the vortex densities. Such singular behavior complicates the application of standard linear stability analysis. In this paper, as a first step towards dealing with these dynamical phenomena, we analyze the dynamical stability of a front between vortices and antivortices. In particular we focus on the question of whether an instability of the vortex front can occur in the absence of a coupling to the temperature. Borrowing ideas developed for singular bacterial growth fronts, we perform an explicit linear stability analysis which shows that, for sufficiently large front velocities and in the absence of coupling to the temperature, such vortex fronts are stable even in the presence of in-plane anisotropy. This result differs from previous conclusions drawn on the basis of approximate calculations for stationary fronts. As our method extends to more complicated models, which could include coupling to the temperature or to other fields, it provides the basis for a more systematic stability analysis of nonlinear vortex front dynamics.