(University of Pittsburgh)
The theoretical and experimental discovery of topological insulators of higher multipole nature, dubbed “higher order topological insulators”, has triggered heated discussions in recent studies. But so far, researches have chiefly been limited to static systems due to the lack of higher order topological invariants constructed for a genuine dynamical system. Here, we report Floquet-driven models showing the anomalous corner states and a construction of dynamical charge polarization of higher order nature. More generically, we proposed characterizing the topology using higher order dynamical singularities, which coincide with results given by Floquet-Wilson loop constructions. Finally, a cold atom experiment scheme is proposed, which would detect not only the existence of corner states, but also their dynamical origin, which has been absent from previous experiments in all kinds of platforms.