The Fermi gerbe of Weyl semimetals

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” geo...

Full description

Saved in:
Bibliographic Details
Published in:Letters in mathematical physics 2021-06, Vol.111 (3), Article 72
Main Authors: Carey, Alan, Thiang, Guo Chuan
Format: Article
Language:English
Subjects:
Complex Systems
Fermi surfaces
Geometry
Group Theory and Generalizations
Hilbert space
Interpolation
Mathematical and Computational Physics
Metalloids
Operators
Physics
Physics and Astronomy
Solid state physics
Theoretical
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01414-0