Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems

Junren Shi, G. Vignale, Di Xiao, Qian Niu

Published 2007-04-29, updated 2007-09-21Version 2

Based on standard perturbation theory, we present a full quantum derivation of the formula for the orbital magnetization in periodic systems. The derivation is generally valid for insulators with or without a Chern number, for metals at zero or finite temperatures, and at weak as well as strong magnetic fields. The formula is shown to be valid in the presence of electron-electron interaction, provided the one-electron energies and wave functions are calculated self-consistently within the framework of the exact current and spin density functional theory.