Landau level states on a topological insulator thin film

TL;DR

This paper investigates Landau level states on topological insulator thin films, revealing surface-localized Landau levels, their dependence on film thickness and magnetic field, and the existence of new surface-bound levels.

Contribution

It provides an analytical and numerical analysis of surface Landau levels, including hybridization effects and surface localization, in topological insulator thin films under magnetic fields.

Findings

Surface Landau levels are decoupled from bulk states.

Hybridization gap depends on film thickness and magnetic field.

Surface Landau levels are localized within one quintuple layer.

Abstract

We analyze the four-dimensional Hamiltonian proposed to describe the band structure of the single-Dirac-cone family of topological insulators in the presence of a uniform perpendicular magnetic field. Surface Landau level(LL) states appear, decoupled from the bulk levels and following the quantized energy dispersion of a purely two-dimensional surface Dirac Hamiltonian. A small hybridization gap splits the degeneracy of the central n=0 LL with dependence on the film thickness and the field strength that can be obtained analytically. Explicit calculation of the spin and charge densities show that surface LL states are localized within approximately one quintuple layer from the surface termination. Some new surface-bound LLs are shown to exist at a higher Landau level index.