Dynamics of a Vortex in Two-Dimensional Superfluid He3-A: Force Caused by the l-Texture

TL;DR

This paper derives the vortex dynamics in superfluid He3-A with l-texture, revealing a Magnus-type force dependent on vortex configuration, and extends the formulation to anisotropic superconductors affecting Hall currents.

Contribution

It introduces a new equation of motion for vortices in superfluid He3-A incorporating the l-texture, with explicit force expressions based on topological mapping.

Findings

Magnus-type force depends on vortex configuration

Explicit force expression in terms of topological degree

Application to anisotropic superconductors shows Hall current variations

Abstract

Based on the Landau-Ginzburg Lagrangian, the dynamics of a vortex is studied for superfluid He3-A characterized by the l-texture. The resultant equation of motion for a vortex leads to the Magnus-type force caused by the l-texture. The force is explicitly written in terms of the mapping degree from the compactified 2-dimensional plane to the space of l-vector, which reflects the quantitative differences of vortex configurations, especially the Mermin-Ho and Anderson-Toulouse vortices. The formulation is applied to anisotropic superconductors in which the Hall current is shown to incorporate changes between vortex configurations.