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The cohomology invariant for class DIII topological insulators

Mathematical Physics 2022-09-28 v1 math.MP

Abstract

This work concerns with the description of the topological phases of band insulators of class DIII by using the equivariant cohomology. The main result is the definition of a cohomology class for general systems of class DIII which generalizes the well known Z2\mathbb{Z}_2-invariant given by the Teo-Kane formula in the one-dimension case. In the two-dimensional case this cohomology invariant allows a complete description of the strong and weak phases. The relation with the KR-theory, the Noether-Fredholm index and the classification of "Real" gerbes are also discussed.

Keywords

Cite

@article{arxiv.2104.00603,
  title  = {The cohomology invariant for class DIII topological insulators},
  author = {Giuseppe De Nittis and Kiyonori Gomi},
  journal= {arXiv preprint arXiv:2104.00603},
  year   = {2022}
}

Comments

38 pages. Keywords: Class DIII topological insulators, "Quaternionic" vector bundles, equivariant cohomology, KR-theory