Attachment of Surface Fermi Arcs to the Bulk Fermi Surface: Fermi-Level Plumbing in Topological Metals

The role of Fermi arc surface-quasiparticle states in topological metals (where some Fermi surface sheets have non-zero Chern number) is examined. They act as Fermi-level plumbing conduits that transfer quasiparticles among groups of apparently-disconnected Fermi sheets with non-zero Chern numbers to maintain equality of their chemical potentials, which is required by gauge invariance. Fermi arcs have a chiral tangential attachment to the surface projections of sheets of the bulk Fermi Surface: the total Chern number of each projection equals the net chirality of arc-attachments to it. Information from the Fermi arcs is needed to unambiguously determine the quantized part of the anomalous Hall effect that is not determined at the bulk Fermi surface.