Connection topology of step edge state bands at the surface of a three dimensional topological insulator

TL;DR

This paper investigates the formation and connectivity of one-dimensional edge states at step defects on the surface of three-dimensional topological insulators like Bi$_2$Se$_3$, revealing their stable topological link to surface Dirac states.

Contribution

It provides numerical simulations demonstrating the topological connection between 1D edge states at step defects and 2D surface Dirac states in topological insulators.

Findings

Edge states are stable and topologically connected to surface Dirac points.

Step defects host localized one-dimensional states.

Numerical models confirm the phenomenology of edge state formation.

Abstract

Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band gap of Bi$_2$Se$_3$ and Bi$_2$Te$_3$, localized at one dimensional step edges. Here numerical simulations of a topological insulator surface are used to explore the phenomenology of edge state formation at the single-quintuple-layer step defects found ubiquitously on these materials. The modeled one dimensional edge states are found to exhibit a stable topological connection to the two dimensional surface state Dirac point.