Orbital Magnetization as a Local Property

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 an 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 not a bulk property in this sense, M is. We provide its r-space expression for any insulator, even with a nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory. DOI: 10.1103/PhysRevLett.110.087202