Wannier representation of Floquet topological states

Understand

A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled.

• This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator.
• Here we generalize this characterization of topological phases toward periodically driven systems.
• We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet topological insulators, anomalous Floquet topological insulators with micromotion-induced boundary states, and gapless Floquet states realized with topological Floquet operators.