Classification of "Quaternionic" Bloch-bundles: Topological Quantum Systems of type AII
Abstract
We provide a classification of type AII topological quantum systems in dimension d=1,2,3,4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which completely classifies "Quaternionic" vector bundles (a.k.a. "symplectic" vector bundles) in dimension d<4. This invariant takes value in a proper equivariant cohomology theory and, in the case of examples of physical interest, it reproduces the familiar Fu-Kane-Mele index. In the case d=4 the classification requires a combined use of the FKMM-invariant and the second Chern class. Among the other things, we prove that the FKMM-invariant is a bona fide characteristic class for the category of "Quaternionic" vector bundles in the sense that it can be realized as the pullback of a universal topological invariant.
Keywords
Cite
@article{arxiv.1404.5804,
title = {Classification of "Quaternionic" Bloch-bundles: Topological Quantum Systems of type AII},
author = {Giuseppe De Nittis and Kiyonori Gomi},
journal= {arXiv preprint arXiv:1404.5804},
year = {2015}
}
Comments
45 pages, 5 tables. key words: Topological insulators, Bloch-bundle, "Quaternionic" vector bundle, FKMM-invariant, Fu-Kane-Mele index. v2 Title, abstract and introduction have been changed. Several typos have been fixed. Journal of reference Commun. Math. Phys