3D Network Model for Strong Topological Insulator Transitions

TL;DR

This paper introduces a 3D network model that captures strong and weak topological insulator phases, demonstrating phase transitions and critical behavior, thus extending the understanding of topological phase transitions from 2D to 3D.

Contribution

It develops a novel 3D network model that explicitly includes strong topological insulator phases and analyzes their phase transitions under disorder.

Findings

Strong topological insulator phases emerge between trivial and weak phases.

A non-local transformation relates trivial and weak phases, with strong phases invariant.

Disorder induces phase transitions from strong topological insulators to metallic phases.

Abstract

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological insulator phase already accommodated by the network model framework in the pre-existing literature, it hosts strong topological insulator phases as well. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a non-local transformation that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this transformation. We show that upon adding sufficiently strong disorder the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semi-classical percolation picture of topological phase transitions in 2D can be generalized to 3D and opens up a new venue for studying 3D topological phase transitions.