Disentangling Orbital Magnetic Susceptibility with Wannier Functions

TL;DR

This paper introduces a new method using modified Wannier functions to decompose orbital magnetic susceptibility into band-specific contributions, enhancing understanding and computational approaches.

Contribution

It presents a novel formula for decomposing susceptibility into intraband, interband, itinerant, and local contributions using Wannier functions, validated in simple models.

Findings

Decomposition quality depends on Wannier function localization.

The formula complements existing methods using Bloch functions.

Clarifies the relationship to Berry curvature.

Abstract

Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a formula to decompose the susceptibility into the contributions from each band. Here, we propose a scheme to perform this decomposition using the modified Wannier functions. The derived formula nicely decomposes the susceptibility into intraband and interband contributions, and from the other aspect, into itinerant and local contributions. The validity of the formula is tested in a couple of simple models. Interestingly, it is revealed that the quality of the decomposition depends on the degree of localization of the used Wannier functions. The formula here complements another formula using Bloch functions, or the formula derived in the semiclassical theory, which deepens our understanding of the orbital magnetic susceptibility and may serve as a foundation of a better computational method. The relationship to the Berry curvature in the present scheme is also clarified.