Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

TL;DR

This paper uses a bi-local mean field approach to study charged and neutral vortex excitations in the fractional quantum Hall state at filling factor 1/3, revealing their properties and energy dependencies.

Contribution

It introduces a numerical mean field framework to analyze vortex excitations, including charged and neutral vortices, in the fractional quantum Hall effect.

Findings

Charged vortex has fractional charge and angular momentum.

Neutral vortex is a bound state of two charged vortices with zero charge.

Neutral vortex creation energy is about half of charged vortex pair creation energy.

Abstract

Applying a bi-local mean field approximation to the fractional quantum Hall state of $\nu=1/3$, we obtain charged and neutral vortex mean field solutions numerically. We calculate the mean field energy and the fluctuation corrections. The charged vortex has a fractional charge and a fractional angular momentum. The neutral vortex is a bound state of two charged vortices and has a zero charge and a zero angular momentum. The creation energy of the neutral vortex is about a half of the pair creation energy of two charged vortices. The magnetic field dependence of the gap energy agrees with the Laughlin's quasiparticle gap energy.