The cohomology invariant for class DIII topological insulators

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 ${\mathbb{Z}}_2$-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.

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

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Cited by in corpus (2)

• Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions
• A new light on the FKMM invariant and its consequences