Phase transitions and scale invariance in topological Anderson insulators

TL;DR

This paper studies disorder-induced topological phase transitions in 2D insulators, revealing a universal scaling behavior of a local topological marker near the transition point, supported by numerical and theoretical analysis.

Contribution

It introduces a single-parameter scaling law for disorder-driven topological transitions using the local Chern marker, supported by numerical simulations and theoretical predictions.

Findings

Disorder-driven transitions are characterized by a single-parameter scaling law.

The critical disorder strength scales as the square root of the Dirac mass.

Numerical results agree with first-order Born approximation predictions.

Abstract

We investigate disordered-driven transitions between trivial and topological insulator (TI) phases in two-dimensional (2D) systems. Our study primarily focuses on the BHZ model with Anderson disorder, while other standard 2DTI models exhibit equivalent features. The analysis is based on the local Chern marker (LCM), a local quantity that allows for the characterization of topological transitions in finite and disordered systems. Our simulations indicate that disorder-driven trivial to topological insulator transitions are nicely characterized by $\mathcal{C}_0$, the disorder averaged LCM near the central cell of the system. We show that $\mathcal{C}_0$ is characterized by a single-parameter scaling, namely, $\mathcal{C}_0(M, W, L) \equiv \mathcal{C}_0(z)$ with $z = [W^\mu-W_c^\mu(M)]L$, where $M$ is the Dirac mass, $W$ is the disorder strength and $L$ is the system size, while $W_c(M) \propto \sqrt{M}$ and $\mu \approx 2$ stand for the critical disorder strength and critical exponent, respectively. Our numerical results are in agreement with a theoretical prediction based on a first-order Born approximation (1BA) analysis. These observations lead us to speculate that the universal scaling function we have found is rather general for amorphous and disorder-driven topological phase transitions.