Equilibrium Surface Current and Role of U(1) Symmetry: sum rule and surface perturbations

TL;DR

This paper investigates how surface perturbations influence equilibrium surface currents and orbital magnetization, revealing that in U(1) symmetric systems these are protected by a sum rule, unlike in superfluids.

Contribution

It demonstrates that surface currents in U(1) conserving systems are robust against surface perturbations due to a sum rule, contrasting with superfluids where such protection is absent.

Findings

Surface currents are unaffected by surface disorder in U(1) systems.

Superfluids lack the sum rule, making surface currents sensitive to surface details.

The sum rule is analogous to Luttinger's theorem, ensuring robustness in certain systems.

Abstract

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 On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.