'Real' gerbes and Dirac cones of topological insulators
High Energy Physics - Theory
2021-11-19 v2 Mesoscale and Nanoscale Physics
Mathematical Physics
Differential Geometry
K-Theory and Homology
math.MP
Abstract
A time-reversal invariant topological insulator occupying a Euclidean half-space determines a 'Quaternionic' self-adjoint Fredholm family. We show that the discrete spectrum data for such a family is geometrically encoded in a non-trivial 'Real' gerbe. The gerbe invariant, rather than a na\"ive counting of Dirac points, precisely captures how edge states completely fill up the bulk spectral gap in a topologically protected manner.
Keywords
Cite
@article{arxiv.2103.05350,
title = {'Real' gerbes and Dirac cones of topological insulators},
author = {Kiyonori Gomi and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2103.05350},
year = {2021}
}
Comments
57 pages, 3 figures, revised version for publication in CMP