| Summary: | Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mi>w</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>w</mi> <mi>π</mi> </msub> <mo stretchy="false">)</mo> <mo>∈</mo> <mn>2</mn> <mi mathvariant="double-struck">Z</mi> <mo>×</mo> <mn>2</mn> <mi mathvariant="double-struck">Z</mi> </mrow> </semantics> </math> </inline-formula>. Under the open boundary condition, these invariants further predict the number of zero- and <inline-formula> <math display="inline"> <semantics> <mi>π</mi> </semantics> </math> </inline-formula>-quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.
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