Computation of topological phase diagram of disordered Pb_{1−x}Sn_{x}Te using the kernel polynomial method

We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than 10^{7} degrees of freedom. Our method enables the study of large complex compounds, where disorder is inherent to the system. We use it to analyze Pb_{1−x}Sn_{x}Te and tighten the critical concentration for the phase transition. Moreover, we obtain the topological phase diagram for related alloys in the family of three-dimensional mirror Chern insulators.