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We investigate disordered-driven transitions between trivial and topologicalinsulator (TI) phases in two-dimensional (2D) systems. Our study primarilyfocuses on the BHZ model with Anderson disorder, while other standard 2DTImodels exhibit equivalent features. The analysis is based on the local Chernmarker (LCM), a local quantity that allows for the characterization oftopological transitions in finite and disordered systems. Our simulationsindicate that disorder-driven trivial to topological insulator transitions arenicely characterized by $\mathcal{C}_0$, the \textit{disorder averaged} LCMnear the central cell of the system. We show that $\mathcal{C}_0$ ischaracterized 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 Diracmass, $W$ 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 strengthand critical exponent, respectively. Our numerical results are in agreementwith a theoretical prediction based on a first-order Born approximation (1BA)analysis. These observations lead us to speculate that the universal scalingfunction we have found is rather general for amorphous and disorder-driventopological phase transitions.

Phase transitions and scale invariance in topological Anderson insulators