Orbital Magnetization in Molecules and in Condensed Matter

Raffaello Bianco, Raffaele Resta

Published 2015-08-05Version 1

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; its relationships with the known $\bf{k}$-space formulas for crystalline insulators are also discussed.