Gapless interface states at the junction between two topological insulators

TL;DR

This paper investigates the properties of interface states at the junction of two topological insulators, revealing conditions for gapless states and clarifying the non-existence of claimed tachyonic excitations.

Contribution

It demonstrates the existence of gapless interface states under broader conditions and clarifies misconceptions about tachyonic excitations at topological insulator interfaces.

Findings

Gapless interface states can exist with both opposite and same helicity orientations.

The existence of interface states correlates with the closing of the bulk gap during helicity change.

Tachyonic excitations at the interface do not exist as previously claimed.

Abstract

We consider a junction between two topological insulators, and calculate the properties of the interface states with an effective low energy Hamiltonian for topological insulators with a single cone on the surface. This system bears a close resemblance to bilayer graphene, as both result from the hybridization of Dirac cones. We find gapless interface states not only when the helicity direction of the topological surface states are oppositely oriented, but they can also exist if they are equally oriented. Furthermore, we find that the existence of the interface states can be understood from the closing of the bulk gap when the helicity changes orientation. Recently, superluminal tachyonic excitations were also claimed to exist at the interface between topological insulators. However, here we show that these interface states do not exist.