The Fermi gerbe of Weyl semimetals
Publication Name
Letters in Mathematical Physics
Abstract
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.
Open Access Status
This publication may be available as open access
Volume
111
Issue
3
Article Number
72
Funding Number
DP200100729
Funding Sponsor
Australian Research Council