The K-Theoretic Bulk–Edge Correspondence for Topological Insulators

Chris Bourne , Johannes Kellendonk (1, 2) , Adam Rennie

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique

We study the application of Kasparov theory to topological insulator systems and the bulk–edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real $C^*$ -algebras and KKO-theory must be used.

Domains: General Physics [physics.gen-ph]

Chris Bourne, Johannes Kellendonk, Adam Rennie. The K-Theoretic Bulk–Edge Correspondence for Topological Insulators. Annales Henri Poincaré, 2017, 18 (5), pp.1833-1866. ⟨10.1007/s00023-016-0541-2⟩. ⟨hal-01555146⟩