The Fermi gerbe of Weyl semimetals

Alan Carey, Guo Chuan Thiang*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    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.

    Original languageEnglish
    Article number72
    JournalLetters in Mathematical Physics
    Volume111
    Issue number3
    DOIs
    Publication statusPublished - Jun 2021

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