Recipe for creating an arbitrary number of Floquet chiral edge states

Abstract

Floquet states of periodically driven systems could exhibit rich topological properties. Many of them are absent in their static counterparts. One such example is the chiral edge states in anomalous Floquet topological insulators, whose description requires a new topological invariant and a novel type of bulk-edge correspondence. In this work, we propose a prototypical quenched lattice model, whose two Floquet bands could exchange their Chern numbers periodically and alternatively via touching at quasienergies 0 and $π$ under the change of a single system parameter. This process in principle allows the generation of as many Floquet chiral edge states as possible in a highly controllable manner. The quantized transmission of these edge states are extracted from the Floquet scattering matrix of the system. The flexibility in controlling the number of topological edge channels provided by our scheme could serve as a starting point for the engineering of robust Floquet transport devices.