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

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 On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.

16 pages

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• Multiply quantized vortices in fermionic superfluids: angular momentum, unpaired fermions, and spectral asymmetry
• Edge current and orbital angular momentum of chiral superfluids revisited
• Two No-Go Theorems on Superconductivity
• Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids
• Interband interference effects at the edge of a multiband chiral p-wave superconductor
• Fulde-Ferrell state in ferromagnetic chiral superconductor with magnetic domain wall
• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class
• Examining the possibility of chiral superconductivity in Sr${}_2$RuO${}_4$ and other compounds via applied supercurrent
• Persistent current-carrying state of charge quasuparticles in $np$-ribbon featuring single Dirac cone