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

TL;DR

This paper explores how Fermi arc surface states in topological metals connect to bulk Fermi surfaces, acting as conduits that maintain chemical potential equality and influence the anomalous Hall effect.

Contribution

It introduces the concept of 'Fermi-level plumbing' showing how Fermi arcs link disconnected Fermi sheets with non-zero Chern numbers, ensuring gauge invariance.

Findings

Fermi arcs connect bulk Fermi surface sheets with non-zero Chern numbers.

Fermi arcs transfer quasiparticles to maintain chemical potential equality.

Fermi arc information is essential for determining the quantized anomalous Hall effect.

Abstract

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.