Alexis Drouot (University of Washington)
Dirac equations at the core of topological insulators
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.