Orbital Magnetization as a Local Property

TL;DR

This paper derives a real-space expression for orbital magnetization in insulators, demonstrating it as an intrinsic bulk property independent of boundary conditions, validated through model simulations.

Contribution

It provides the first real-space formulation of orbital magnetization applicable to insulators with nonzero Chern invariant, independent of boundary conditions.

Findings

Derived a real-space expression for orbital magnetization.

Validated the theory with simulations on a model Hamiltonian.

Showed orbital magnetization as a true bulk property.

Abstract

The modern expressions for polarization $\P$ and orbital magnetization $\M$ are $\k$-space integrals. But a genuine bulk property should also be expressible in $\r$-space, as unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions---either periodic or open. While $\P$---owing to its "quantum" indeterminacy---is {\it not} a bulk property in this sense, $\M$ is. We provide its $\r$-space expression for any insulator, even with nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory.