Topological quantum phase transitions in topological insulator thin film

TL;DR

This paper explores topological quantum phase transitions in a three-dimensional topological insulator thin film model, analyzing how various interactions induce different topological phases and associated gap closing points.

Contribution

It introduces a comprehensive tight binding model capturing multiple topological phases and transitions in TI thin films, including effects of magnetic fields and spin-orbit coupling.

Findings

Identification of quantum spin Hall and quantum anomalous Hall phases.

Demonstration of phase transitions linked to gap closing points.

Edge state analysis confirming topological phases.

Abstract

Topological quantum phase transition in electron gas systems is an enthralling phenomena. This phase transition has a unique property in that it is associated with a quantum phase transition point, which separates different regions with gapped phases, characterized by an immutable topological quantity called the Chern number. In this paper, we study a tight binding model for a three-dimensional topological insulator $(TI)$ thin film that captures different topological quantum phase transitions in the entire Brillouin zone. We investigate the effects of a staggered magnetic field, an off-diagonal coupling term, and a Rashba spin-orbit coupling $(SOC)$ on the topological insulator thin film model. We give a lucid exposition of the topological phases by exploring all the topological properties of this system in the entire Brillouin zone, as a function of the competing interactions. We find that the system exhibits quantum spin Hall $(QSH)$ phase, quantum anomalous Hall $(QAH)$, semi-metallic phase, and an ordinary insulator phase. The transition from one phase to another is invariably associated with a gap closing point. We further corroborate our results by solving for the edge states modes of the system.