Interacting Dirac Fermions on a Topological Insulator in a Magnetic Field

TL;DR

This paper investigates the fractional quantum Hall effect on the surface of topological insulator thin films under magnetic fields, highlighting how finite thickness and surface interactions influence observable quantum states.

Contribution

It provides the first detailed analysis of fractional quantum Hall states on topological insulator surfaces, considering effects of film thickness and surface level mixing.

Findings

Fractional quantum Hall states are observable on topological insulator surfaces.

Excitation gaps depend non-monotonically on film thickness.

Gaps in the lowest Landau levels become comparable at large thickness.

Abstract

We have studied the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently. Our studies indicate that the fractional quantum Hall states should indeed be observable in the surface Landau levels of a topological insulator. The strength of the effect will however be different, compared to that in graphene, due to the finite thickness of the topological insulator film and due to the admixture of Landau levels of the two surfaces of the film. At a small film thickness, that mixture results in a strongly non-monotonic dependence of the excitation gap on the film thickness. At a large enough thickness of the film, the excitation gap in the lowest two Landau levels are comparable in strength.