Floquet Hopf Insulators

We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf \mathbb{Z}invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet \mathbb{Z}_2invariant, and represents a condensed matter realization of the topology...