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

TL;DR

This paper introduces a coupling-matrix method for efficiently calculating the Chern number in both crystalline and disordered two-dimensional systems, accurately capturing topological phases and disorder-induced transitions.

Contribution

The paper presents a novel, fast coupling-matrix approach for computing Chern numbers applicable to disordered systems, improving efficiency and accuracy over existing methods.

Findings

Successfully applied to Haldane and Hofstadter models

Accurately reproduces disorder-induced topological phase transitions

Demonstrates wide applicability to topological quantum number studies

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.