Title: Floquet Hamiltonians - effective gaps and resonant decay
Speaker: Amir Sagiv (Columbia University)
Speaker's URL: http://www.columbia.edu/~as6011/
Abstract: Floquet topological insulators are an emerging category of materials whose properties are transformed by time-periodic forcing. Can their properties be understood from their first-principles continuum models, i.e., 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 metastable. 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.