qth-root non-Hermitian Floquet topological insulators

Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer qth-root of the evolution operator U that describes Floquet 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 fractional quasienergies ±(0, 1, ...2ⁿ)π/2ⁿ and ±(0, 1, ..., 3ⁿ)π/3ⁿ, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, 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.