Localization of spinwaves in the quantum Hall ferromagnet

TL;DR

This paper studies how spinwaves in a quantum Hall ferromagnet become localized due to disorder, using a non-linear sigma model, and suggests experimental detection via photoluminescence.

Contribution

It introduces a theoretical framework linking spinwave localization to topological charge density and disorder, providing new insights into quantum Hall ferromagnet properties.

Findings

All states in the model are localized in two dimensions.

A connection between topological density and charge density is established.

Experimental signatures in photoluminescence are proposed.

Abstract

The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual properties due to the remarkable identity between the topological density of a spin distortion and the associated electrical charge density. We investigate the localization of spinwaves by coupling to a scalar disorder potential via their topological density. A low energy description of the system in terms of a non-linear sigma model of unitary supermatrices is derived. All states of this model are localized in two dimensions. A possible experimental signature of these effects in photo-luminescence is suggested.