qth-root non-Hermitian Floquet topological insulators

Floquet phases of matter have attracted great attention due to their dynamical and topo-logical nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer q th-root of the evolution operator U that describes Flo-quet topological matter. We further apply our qth-rooting procedure to obtain 2nth-and 3nth-root first-and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at frac-tional quasienergies +/-(0, 1, ...2n)7r/2n and +/-(0, 1, ..., 3n)7r/3n, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. No-tably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.