Symmetry analysis of anomalous Floquet topological phases

The topological characterization of nonequilibrium matter is highly nontrivial because familiar approaches designed for equilibrium phases may not apply. In the presence crystal symmetry, Floquet insulator states cannot be easily distinguished from normal insulators by a set symmetry eigenvalues at high points in Brillouin zone. This work advocates physically motivated, easy-to-implement approach to enhance analysis distinguish between variety phases. Using two-dimensional inversion-symmetric periodically-driven system as an example, we show that anomalous states, both first-order and second-order, are same atomic insulators. However, can one another inspecting occurrence stable inversion their microscopic dynamics. simple picture understanding how boundary coexist with localized bulk