Edge states of a three-dimensional topological insulator

Abstract

We use the bulk Hamiltonian for a three-dimensional topological insulator such as $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.

13 pages, 10 figures

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• Experimental search for one-dimensional edge states at surface steps of the topological insulator Bi${}_2$Se${}_3$: Distinguishing between effects and artifacts
• Generating surface states in a Weyl semi-metal by applying electromagnetic radiation
• Transport in a thin topological insulator with potential and magnetic barriers
• Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators
• Pseudospin-valve effect on transport in junctions of three-dimensional topological insulator surfaces
• Edge bands and vertical transport in topological insulator/magnetic insulator heterostructures
• Semiclassical scattering by edge imperfections in topological insulators under magnetic field
• Electronic confinement of surface states in a topological insulator nanowire
• Friedel sum rule in the presence of topological defects for graphene