Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

TL;DR

This paper develops a Ginzburg-Landau model for charged vortices in 2+1 dimensions, analyzing their classical and quantum dynamics, and revealing their behavior in the lowest Landau level and boundary effects.

Contribution

It introduces a collective coordinate approach for charged vortices in the Ginzburg-Landau framework and explores their classical and quantum dynamics, including boundary effects.

Findings

Vortices are shown to be charged entities.

Quantum vortex motion occurs in the lowest Landau level.

Boundary effects influence vortex dynamics.

Abstract

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.