Real-Space Spectral Approach to Orbital Magnetization

TL;DR

This paper introduces a real-space spectral method for calculating orbital magnetization in crystals, enabling efficient analysis of large, disordered, and temperature-affected systems without eigenstate computations.

Contribution

The authors develop a spectral function approach using Chebyshev expansions for orbital magnetization, applicable to large and complex systems, and connect magnetization spectral density to topological invariants.

Findings

Accurate magnetization results for the Haldane model

Extension to disordered and defect-laden systems

Direct extraction of Chern number from spectral density

Abstract

We present a real-space spectral method for computing the orbital magnetization of crystals. Starting from the commutator form of the orbital magnetization operator, we formulate an energy-resolved spectral function that is amenable to exact Chebyshev polynomial expansions and yields the total magnetization upon integration up to the Fermi level. This avoids the need for computing eigenstates and ground-state projects, providing an efficient numerical framework that is applicable to very large systems even in the presence of disorder and temperature. Our approach is benchmarked on the Haldane model, finding results that are in excellent agreement with the modern $k$-space formulation of orbital magnetization. Leveraging this technique, we extend our study to systems with uncorrelated disorder and point defects, and further show that the bulk Chern number can be directly obtained from the magnetization spectral density. These results open a promising route to investigate orbital responses and topological transitions in real-space models of quantum materials with realistic complexity.