Alexis Drouot (University of Washington)

Dirac equations at the core of topological insulators

Abstract: Topological insulators are fascinating materials that block conduction in their interior but enhance it unidirectionally along their boundaries. In this talk, I will explain how a universal class of Dirac equations emerge from elementary models. I will then show that (suitably localized) waves propagate coherently along boundaries in a prescribed direction; but disperse when forcing propagation in the opposite one. This study is closely connected to the semiclassical analysis of systems whose (matrix-valued) symbols admit eigenvalue crossings. I will then illustrate the results with various numerical simulations. Joint work with Bal, Becker, Fermanian Kammerer, Lu and Watson.