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Floquet topological insulators are an important category of materials whose properties are transformed by time-periodic forcing. Can their properties be understood from their first-principles continuum (PDE) models, e.g., from a driven Schrodinger equation?
First, we study the transformation of graphene from a conductor into an insulator under a time-periodic magnetic potential. We show that the dynamics of certain wave-packets are governed by a Dirac equation, which has a spectral gap property. This gap is then carried back to the original Schrodinger equation in the form of an “effective gap” - a new and physically-relevant relaxation of a spectral gap. Next, we show that, due to resonance, localized modes in periodically-forced media are only metasable. Sufficiently rapid forcing couples the localized mode to the bulk, and so energy eventually leaks away from the localized edge/defect, in the spirit of the Fermi Golden Rule.

Possibly also at: https://ucdavis.zoom.us/j/94506910050