A toy model for quantum spin Hall effect

TL;DR

This paper introduces a simplified model of a 3D topological insulator surface coupled to a pseudo spin-1/2 particle, capturing key features like topological phase transition and quantum spin Hall effect, and explores magnetic field effects.

Contribution

It presents a novel toy model that reproduces essential topological insulator surface phenomena, including phase transitions and Landau levels, providing insights into their underlying physics.

Findings

Model reproduces topological quantum phase transition

Captures quantum spin Hall effect features

Derives Landau levels under magnetic field

Abstract

In this Communication, we investigate a toy model of three-dimensional topological insulator surface, coupled homogeneously to a fictitious pseudo spin-$\frac{1}{2}$ particle. We show that this toy model captures the interesting features of topological insulator surface states, which include topological quantum phase transition and quantum spin hall effect. We further incorporate an out-of-plane magnetic field and obtain the Landau levels.