$q$th-root non-Hermitian Floquet topological insulators

Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique nonequilibrium settings. In this work, we introduce a generic way taking any integer q q th-root the evolution operator U display="inline">U describes matter. We further apply our th-rooting procedure obtain 2^n display="inline">2n th- 3^n display="inline">3n first- second-order non-Hermitian insulators~(FTIs). There, explicitly demonstrate presence multiple edge corner modes at fractional quasienergies \pm(0,1,...2^{n})\pi/2^{n} display="inline">±(0,1,...2n)?/2n \pm(0,1,...,3^{n})\pi/3^{n} form="prefix">(0,1,...,3n)?/3n , whose numbers highly controllable capturable by invariants parent systems. Notably, observe non-Hermiticity induced fractional-quasienergy coexistence skin effect with states. Our findings thus establish framework constructing an intriguing class in open