Higher Order Floquet Topological Insulators with Anomalous Corner States

The theoretical and experimental discovery of topological insulators of higher multipole nature, dubbed “higher order topological insulators” (HOTI), has triggered heated discussions in recent studies. But so far, all researches have been limited to static systems due to the lack of higher order topological invariants constructed for a genuine dynamical system. Here, we report a Floquet-driven model showing the anomalous corner states and a construction of dynamical topological invariant built upon evolution operators $ U(t) $. We show that the bulk static nested quadrupoles, constructed by eigenstates of the static Floquet operator $ U_F = U(T) $, vanish identically, while corner states emerge in all energy gaps with quantized charges due to the dynamical topology. The signature of such an anomalous Floquet phase in cold atom experiments is also discussed via corner particle dynamics and a band tomography. Our work paves the way to the systematic study of HOTI in regimes far away from equilibrium.