Discrete Bound States in a Floquet-Bloch Active Spinning System

Inspired by electronic systems, we explore the transport of an active spinning particle in a lattice of posts using a periodic driving protocol akin to a Floquet system. In our 2D Floquet-Bloch system, coupling of hydrodynamic and electrostatic interactions leads to hybridization of localized states of the spinning particle that are able to diffuse through the medium, or in some cases move ballistically. More interestingly, we find a set of discrete localized states at quantized applied frequencies that delimit regions of diffusion. These states have typical orbits much larger than the original localized states. They occur approximately at fractional frequency values of the two frequencies for the localized trivial states. Our results may be an interesting new view on transport in active colloidal systems and their counterparts in solid state physics.