Helical edge states in multiple topological mass domains

TL;DR

This paper investigates how edge states in two-dimensional topological insulators are affected by multiple mass domains, revealing the dependence of edge state properties on mass ratios and boundary configurations.

Contribution

It provides a detailed analysis of edge modes in the BHZ model with multiple topological and normal insulator domains, highlighting the influence of Dirac mass ratios on edge state behavior.

Findings

Edge state Dirac points depend on mass ratios at boundaries.

Multiple boundary configurations alter edge mode properties.

The study clarifies the impact of finite mass regions on topological edge states.

Abstract

The two-dimensional topological insulating phase has been experimentally discovered in HgTe quantum wells (QWs). The low-energy physics of two-dimensional topological insulators (TIs) is described by the Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a normal insulating phase depends on the Dirac mass being negative or positive, respectively. We solve the BHZ model for a mass domain configuration, analyzing the effects on the edge modes of a finite Dirac mass in the normal insulating region (soft-wall boundary condition). We show that at a boundary between a TI and a normal insulator (NI), the Dirac point of the edge states appearing at the interface strongly depends on the ratio between the Dirac masses in the two regions. We also consider the case of multiple boundaries such as NI/TI/NI, TI/NI/TI and NI/TI/NI/TI.