Weak topological insulator with protected gapless helical states

TL;DR

This paper models how dislocation lines in weak topological insulators host protected gapless helical states, revealing the evolution of surface Dirac cones into stable one-dimensional modes near dislocations.

Contribution

It introduces a model linking dislocation lines to protected gapless states in weak topological insulators, highlighting the role of finite-size gaps and Burgers vectors.

Findings

Dislocation lines induce protected gapless helical states.

Surface Dirac cones develop finite-size gaps under deformation.

Dislocations with non-trivial Burgers vectors stabilize 1D gapless modes.

Abstract

A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap, when the surface is deformed into a cylinder penetrating the otherwise surface-less system. We show that when a dislocation with a non-trivial Burgers vector is introduced, the finite-size energy gap play the role of stabilizing the one-dimensional gapless states.