We discuss effects of surface perturbations on equilibrium surface currents which contribute to orbital magnetization and orbital angular momentum in systems without time-reversal symmetry. We show that, in a U(1) particle-number-conserving system, disorder and other perturbations at a surface do not affect the equilibrium surface current and corresponding orbital magnetization, due to a sum rule which is analogous to Luttinger's theorem. On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.

• Received 5 June 2015
• Revised 27 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.104502