Non-Hermitian Floquet higher-order topological states in two-dimensional quasicrystals

The topological states in non-Hermitian Floquet systems possess intriguing physical phenomena. Unlike crystals, quasicrystals offer a unique platform for exploring topological states. Here, we generalize the non-Hermitian Floquet higher-order topological states to quasicrystals. We develop the non-Hermitian Floquet multipole numbers as a real-space topological invariant to effectively characterize higher-order topology. We establish the physical connection between the different delocalization properties of non-Hermitian Floquet 0 and $\ensuremath{\pi}$ modes and the lattice arrangement of quasicrystals as well as non-Hermitian skin effect. By constructing effective models and evolution equations, we reveal the modulation mechanism and evolution characteristics of non-Hermitian Floquet $\ensuremath{\pi}$ modes in quasicrystals with 12-fold rotational symmetry. Our results demonstrate the flexible tunability of non-Hermitian Floquet topological states in quasicrystals, offering a different avenue for investigating unique physical phenomena and applications of quasicrystals within non-Hermitian Floquet systems.