Orbital Magnetization in Insulators: Bulk vs. Surface

TL;DR

This paper develops a theoretical framework to distinguish bulk and surface contributions to the orbital magnetization in insulators, emphasizing the role of surface states and transverse conductivity, validated by model simulations.

Contribution

It introduces a method to separate bulk and surface orbital magnetization contributions in insulators, highlighting the significance of surface states and conductivity.

Findings

Orbital magnetization decomposes into bulk and surface terms.

Surface contribution appears only with nonzero transverse conductivity.

Model simulations confirm the theoretical predictions.

Abstract

The orbital magnetic moment of a finite piece of matter is expressed in terms of the one-body density matrix as a simple trace. We address a macroscopic system, insulating in the bulk, and we show that its orbital moment is the sum of a bulk term and a surface term, both extensive. The latter only occurs when the transverse conductivity is nonzero and owes to conducting surface states. Simulations on a model Hamiltonian validate our theory.