Dirac Electrons on a Sharply Edged Surface of Topological Insulators

TL;DR

This paper investigates how Dirac electrons on the surface of topological insulators behave at sharp edges, showing they are robust against backscattering and exhibit velocity renormalization near edges.

Contribution

It explicitly constructs the surface Hamiltonian on a hyperbolic surface to analyze electron behavior at sharp edges, revealing robustness against backscattering and velocity changes.

Findings

No backward scattering at a concave 90° step edge.

Velocity of electrons is strongly renormalized near the step edge.

Dirac surface states are smoothly extended over edges despite anisotropy.

Abstract

An unpaired gapless Dirac electron emergent at the surface of a strong topological insulator (STI) is protected by the bulk-surface correspondence and believed to be immune to backward scattering. It is less obvious, however, and yet to be verified explicitly whether such a gapless Dirac state is smoothly extended over the entire surface when the surface is composed of more than a single facet with different orientations in contact with one another at sharp corner edges (typically forming a steplike structure). In the realistic situation that we consider, the anisotropy of the sample leads to different group velocities in each of such facets. Here, we propose that much insight on this issue can be obtained by studying the electronic states on a hyperbolic surface of an STI. By explicitly constructing the surface effective Hamiltonian, we demonstrate that no backward scattering takes place at a concave $90^\circ$ step edge. A strong renormalization of the velocity in the close vicinity of the step edge is also suggested.