We investigate disorder-driven transitions between trivial and topological insulator (TI) phases in two-dimensional (2D) systems. Our study primarily focuses on the Bernevig-Hughes-Zhang (BHZ) model with Anderson disorder, while other standard 2D TI 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, ${\mathcal{C}}_0(M,W,L)\equiv {\mathcal{C}}_0\left(z\right)$, with $z=[W^{\mu }-W_c^{\mu }\left(M\right)]L$, where $M$ is the Dirac mass, $W$ is the disorder strength, and $L$ is the system size, while $W_c\left(M\right)\propto \sqrt{M}$ and $\mu \approx 2$ stand for the critical disorder strength and the critical exponent, respectively. Our numerical results are in agreement with a theoretical prediction based on a first-order Born approximation 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.

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• Chern insulators
• Critical exponents
• Density of states
• Edge states
• Kane-Mele model
• Order parameters
• Phase diagrams
• Spintronics
• Topological insulators
• Topological materials
• Topological phase transition
• Topological phases of matter
• 2-dimensional systems
• Honeycomb lattice
• Tight-binding model
• k dot p method