Density-operator theory of orbital magnetic susceptibility in periodic insulators

TL;DR

This paper introduces a density-operator based framework for calculating orbital magnetic susceptibility in periodic insulators, providing a simple, accurate formula validated through models and numerical analysis.

Contribution

It presents a novel, perturbation-theory-based method for magnetic fields in periodic insulators, extending existing electric field schemes and deriving a simple susceptibility formula.

Findings

Derived a new formula for orbital magnetic susceptibility.

Validated the formula with tight-binding models and numerical simulations.

Achieved excellent agreement between analytical and numerical results.

Abstract

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.