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

Abstract

The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, the quantized Chern numbers being correctly obtained. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.

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• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Robustness of the Spin-Chern number
• Entanglement Spectrum of a Disordered Topological Chern Insulator
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