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Type: Journal article
Title: The Fermi gerbe of Weyl semimetals
Author: Carey, A.
Thiang, G.C.
Citation: Letters in Mathematical Physics, 2021; 111(3):72-1-72-16
Publisher: Springer Nature
Issue Date: 2021
ISSN: 0377-9017
Statement of
Alan Carey, Guo Chuan Thiang
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.
Keywords: Gerbes; spectral flow; topological semimetals
Rights: © The Author(s), under exclusive licence to Springer Nature B.V. 2021
DOI: 10.1007/s11005-021-01414-0
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