'Real' gerbes and Dirac cones of topological insulators

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 naïve counting of Dirac points, precisely captures how edge states completely fill up the bulk spectral gap in a topologically protected manner.

arXiv comment57 pages, 3 figures, revised version for publication in CMP

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