Gapless interface states between topological insulators with opposite Dirac velocities

TL;DR

This paper investigates the electronic states at the interface between two topological insulators with opposite Dirac velocities, revealing the existence of protected gapless states due to mirror symmetry.

Contribution

It demonstrates the conditions under which gapless interface states form between topological insulators with opposite velocities, highlighting the role of mirror symmetry in their protection.

Findings

Interface states exist when velocities have opposite signs.

Mirror symmetry protects the gapless states.

Transmission and reflection are suppressed at normal incidence for opposite velocities.

Abstract

The Dirac cone on a surface of a topological insulator shows linear dispersion analogous to optics and its velocity depends on materials. We consider a junction of two topological insulators with different velocities, and calculate the reflectance and transmittance. We find that they reflect the backscattering-free nature of the helical surface states. When the two velocities have opposite signs, both transmission and reflection are prohibited for normal incidence, when a mirror symmetry normal to the junction is preserved. In this case we show that there necessarily exist gapless states at the interface between the two topological insulators. Their existence is protected by mirror symmetry, and they have characteristic dispersions depending on the symmetry of the system.