Rearrangement of the vortex lattice due to instabilities of vortex flow

TL;DR

This paper investigates how increasing current causes a superconductor's vortex lattice to transition from a triangular structure to parallel vortex rows due to non-equilibrium effects on vortex cores, leading to flow instabilities.

Contribution

It introduces a model explaining vortex lattice rearrangement and flow instability based on non-equilibrium quasiparticle effects within the time-dependent Ginzburg-Landau framework.

Findings

Vortex lattice transforms from triangular to parallel rows with increased current.

Vortex flow instability linked to non-equilibrium quasiparticle distribution.

Formation of quasi-phase slip lines at critical vortex velocity.

Abstract

With increasing applied current we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the vortex core due to non-equilibrium effects (similar to the mechanism of vortex motion instability in the Larkin-Ovchinnikov theory). The moving vortex creates a deficit of quasiparticles in front of its motion and an excess of quasiparticles behind the core of the moving vortex. This results in the appearance of a wake (region with suppressed order parameter) behind the vortex which attracts other vortices resulting in an effective direction-dependent interaction between vortices. When the vortex velocity $v$ reaches the critical value $v_c$ quasi-phase slip lines (lines with fast vortex motion) appear which may coexist with slowly moving vortices between such lines. Our results are found within the framework of the time-dependent Ginzburg-Landau equations and are strictly valid when the coherence length $\xi(T)$ is larger or comparable with the decay length $L_{in}$ of the non-equilibrium quasiparticle distribution function. We qualitatively explain experiments on the instability of vortex flow at low magnetic fields when the distance between vortices $a \gg L_{in} \gg \xi (T)$. We speculate that a similar instability of the vortex lattice should exist for $v>v_c$ even when $a<L_{in}$.