Mardi 28 novembre 2023 à 11h00 / Amphithéâtre François Canac, LMA
Abstract : One of humanity’s most ambitious current challenges concerns the possibility of structuring matter at different scales to obtain, at the macroscopic level, unusual physical properties with respect to wave propagation phenomena. In this regard, a large number of fields of physics and engineering have been involved, such as the study of the propagation of electrons in graphene sheets, and the conception of photonic and phononic crystals to prevent the propagation, in certain frequency intervals (band-gaps), of electromagnetic or acoustic/elastic waves. Specifically, the possibility of preventing or controlling wave propagation is intimately connected to certain topological invariants emerging from the periodicity of the underlying crystal structure. In this talk, I want to discuss which types of topological obstructions prevent the existence of crystallographic invariant exponentially localized Wannier functions in topological insulators. As long as crystallographic groups are involved, twists in the ordinary K-theory must be considered. The problem has then to be studied in the more general framework of twisted K-theory.