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The Chern number is often used to distinguish between different topologicalphases of matter in two-dimensional electron systems. A fast and efficientcoupling-matrix method is designed to calculate the Chern number in finitecrystalline and disordered systems. To show its effectiveness, we apply theapproach to the Haldane model and the lattice Hofstadter model, the quantizedChern numbers being correctly obtained. The disorder-induced topological phasetransition is well reproduced, when the disorder strength is increased beyondthe critical value. We expect the method to be widely applicable to the studyof topological quantum numbers.

Coupling-Matrix Approach to the Chern Number Calculation in Disordered Systems