Non-Hermitian Floquet Topological Matter -- A Review

Non-Hermitian Floquet topological phases appear in systems described by time-periodic non-Hermitian Hamiltonians. This review presents a sum-up of our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. After a brief overview of the literature, we introduce our theoretical framework for the study of non-Hermitian Floquet systems and the topological characterization of non-Hermitian Floquet bands. Based on our theories, we describe typical examples of non-Hermitian Floquet topological insulators, superconductors and quasicrystals with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties and localization transitions. We conclude this review by summarizing our main discoveries and discussing potential future directions.