One-dimensional Dirac electrons on the surface of weak topological insulators

TL;DR

This paper demonstrates that weak three-dimensional topological insulators host topologically protected one-dimensional Dirac electrons along specific surface directions, characterized by line-like energy dispersions due to in-plane time-reversal symmetry.

Contribution

It introduces the concept of in-plane time-reversal invariance as a symmetry protecting Dirac line degeneracies on the surface of weak topological insulators.

Findings

Dirac lines are topologically protected by in-plane time-reversal symmetry.

Surface Dirac lines appear in stacked Kane-Mele models and similar weak topological insulators.

The surface spectrum features line-like energy dispersions along certain Brillouin zone directions.

Abstract

We show that a class of weak three-dimensional topological insulators feature one-dimensional Dirac electrons on their surfaces. Their hallmark is a line-like energy dispersion along certain directions of the surface Brillouin zone. These one-dimensional Dirac line degeneracies are topologically protected by a symmetry that we refer to as in-plane time-reversal invariance. We show how this invariance leads to Dirac lines in the surface spectrum of stacked Kane-Mele systems and more general models for weak three-dimensional topological insulators.