Anderson localization in fractional quantum Hall effect

TL;DR

This paper provides theoretical evidence linking quasiparticle localization in fractional quantum Hall states to electron localization in higher Landau levels, predicting critical energies and localization length divergence.

Contribution

It introduces a novel correspondence between quasiparticle localization in fractional quantum Hall states and electron localization in Landau levels, with implications for understanding extended states.

Findings

Localization of quasiparticles mirrors electron localization in higher Landau levels.

Predictions of extended states at critical energies in fractional quantum Hall regime.

Divergence of localization length near critical energies.

Abstract

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $\nu=n/(2n+1)$ has a striking {\it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.