Properties of Quantum Hall Skyrmions from Anomalies

TL;DR

This paper develops a theoretical framework for understanding quantum Hall Skyrmions by coupling Chern-Simons theory with topological spin currents and anomaly considerations, determining their charge and spin properties.

Contribution

It introduces a novel coupling of Chern-Simons theory with topological spin currents and anomaly cancellation to precisely determine Skyrmion charge and spin in quantum Hall systems.

Findings

Charge of Skyrmion is eνN_{Sky}

Spin of Skyrmion is (νN_{Sky})/2

Classical spin fluctuations follow ferromagnet equations

Abstract

It is well known that the Fractional Quantum Hall Effect (FQHE) may be effectively represented by a Chern-Simons theory. In order to incorporate QH Skyrmions, we couple this theory to the topological spin current, and include the Hopf term. The cancellation of anomalies for chiral edge states, and the proviso that Skyrmions may be created and destroyed at the edge, fixes the coefficients of these new terms. Consequently, the charge and the spin of the Skyrmion are uniquely determined. For those two quantities we find the values $e\nu N_{Sky}$ and $\nu N_{Sky}/2$, respectively, where $e$ is electron charge, $\nu$ is the filling fraction and $N_{Sky}$ is the Skyrmion winding number. We also add terms to the action so that the classical spin fluctuations in the bulk satisfy the standard equations of a ferromagnet, with spin waves that propagate with the classical drift velocity of the electron.