The Fermi gerbe of Weyl semimetals
Letters in Mathematical Physics
In the gap topology, the unbounded self-adjoint Fredholm operators on a Hilbert space have third homotopy group the integers. We realise the generator explicitly, using a family of Dirac operators on the half-line, which arises naturally in Weyl semimetals in solid-state physics. A “Fermi gerbe” geometrically encodes how discrete spectral data of the family interpolate between essential spectral gaps. Its non-vanishing Dixmier–Douady invariant protects the integrity of the interpolation, thereby providing topological protection of the Weyl semimetal’s Fermi surface.
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Australian Research Council