Delocalization Transition of Disordered Axion Insulator

TL;DR

This paper demonstrates that disordered axion insulators inevitably undergo a delocalization transition with an intermediate metallic phase, maintaining topological robustness under average inversion symmetry and characterized by a specific critical exponent.

Contribution

It introduces a comprehensive analysis of the delocalization transition in disordered axion insulators, combining theoretical, numerical, and effective Hamiltonian approaches.

Findings

An intermediate metallic phase exists during the transition from axion to trivial insulator.

The localization length critical exponent is approximately 1.42.

The delocalization transition remains stable under weak inversion symmetry breaking.

Abstract

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be $\nu=1.42\pm 0.12$. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low energy k$\cdot$p expansion.