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.

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