Orbital magnetization in periodic insulators

TL;DR

This paper derives a gauge-invariant expression for the orbital magnetization of periodic insulators using Wannier functions, revealing both bulk and surface contributions, and verifies it through numerical calculations.

Contribution

It introduces a novel, gauge-invariant formula for orbital magnetization that accounts for surface currents in periodic insulators.

Findings

Bulk and surface contributions to magnetization are both significant.

The derived expression matches numerical tight-binding calculations.

Surface currents contribute to the overall orbital magnetization.

Abstract

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.