The stability of the fractional quantum Hall effect in topological insulators

TL;DR

This paper explores the theoretical feasibility of the fractional quantum Hall effect in topological insulators, highlighting conditions for its occurrence and predicting unique asymmetries due to spin-orbit coupling.

Contribution

It provides a theoretical analysis of the conditions under which fractional quantum Hall effect can occur in topological insulators, emphasizing the role of Landau levels and spin-orbit coupling.

Findings

Fractional quantum Hall effect is feasible in $n=0$ and $|n|=1$ Landau levels.

It is unlikely in higher $|n|$ Landau levels.

Predicted asymmetry between $n=1$ and $n=-1$ levels due to spin-orbit coupling.

Abstract

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the $n=0$ and $|n|=1$ Landau levels, it is ruled out in higher $|n|$ Landau levels. Unlike graphene, the fractional quantum Hall effect in topological insulators is predicted to show an interesting asymmetry between $n=1$ and $n=-1$ Landau levels due to spin-orbit coupling.