Landau level states on a topological insulator thin film

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.

8 pages, 4 figures

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• Probing the wavefunction of the surface states in Bi${}_2$Se${}_3$ topological insulator: a realistic tight-binding approach
• Quantum Hall effect in a singly and doubly connected 3D topological insulator
• Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
• Interacting Dirac Fermions on a Topological Insulator in a Magnetic Field
• Thin films of a three-dimensional topological insulator in a strong magnetic field: a microscopic study
• Electron-Hole Asymmetry of Surface States in Topological Insulator Sb2Te3 Thin Films Revealed by Magneto-Infrared Spectroscopy
• The stability of the fractional quantum Hall effect in topological insulators
• The Fractional Quantum Hall Effect of Tachyons in a Topological Insulator Junction
• Unconventional quantum Hall effect in Floquet topological insulators
• Particle-hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films
• Landau levels on a surface of weak topological insulators
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice