Bifurcation of the Edge-State Width in the Two-Dimensional Topological Insulator

TL;DR

This paper investigates the behavior of edge states in a two-dimensional topological insulator, revealing a bifurcation in their width as they merge with bulk states, with implications for experimental observations.

Contribution

It introduces a theoretical analysis of edge-state width bifurcation in the Kane-Mele model with zigzag boundaries, providing new insights into edge-bulk state transitions.

Findings

Edge states merge into bulk bands via width bifurcation.

Derived coupled equations for energy and edge-state width.

Implications for experiments on monolayer topological insulators.

Abstract

We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite honeycomb lattice with a zigzag boundary. It is revealed that, in a one-dimensional Brillouin zone, the edge states merge into the continuous bands of the bulk states through a bifurcation of the edge-state width. We discuss the implications of the results to the experiments in monolayer or thin films of topological insulators.