Gaps and effective gaps in Floquet media

Applying time-periodic forcing is a common technique to effectively change materials properties. A well-known example is the transformation of graphene from a conductor to an insulator ("Floquet topological insulator'') by applying to it a time-dependent magnetic potential. We will see how this phenomenon is derived from certain reduced models of graphene. We will then turn to the first-principle, continuum, model of graphene. There, it is not at all obvious how to derive the insulation property, or even what its mathematical expression is. We will introduce the notion of an "effective gap", or low-oscillations gap, and prove its existence in forced graphene. This new notion distinguishes a part of the energy-spectrum in a quantitative way. It implies that the medium is approximately insulating to a class of physically-likely wavepackets.

Based on joint work with MI Weinstein.