Numerical Study of Disorder on the Orbital Magnetization in Two Dimensions

TL;DR

This study numerically investigates how disorder affects orbital magnetization in a two-dimensional Haldane model, revealing energy shifts, localization trends, and topological state contributions, with implications for disorder-induced topological metal states.

Contribution

It provides a detailed numerical analysis of disorder effects on orbital magnetization in 2D topological insulators using the Wannier function approach.

Findings

Energy renormalization shifts in weak disorder regime

Localization trend of band orbital magnetization

Enhancement of magnetization at intermediate disorder levels

Abstract

The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistent T-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.