Alexander Fritsche, Bastian Höckendorf, Andreas Alvermann, Holger Fehske

• We present a non-Hermitian Floquet model with topological edge states in real and imaginaryband gaps. The model utilizes two stacked honeycomb lattices which can be related via four different typesof non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides uswith either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap.The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter.In stark contrast, we find that the edgeWe present a non-Hermitian Floquet model with topological edge states in real and imaginaryband gaps. The model utilizes two stacked honeycomb lattices which can be related via four different typesof non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides uswith either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap.The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter.In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remainsspatially localized while its amplitude continuously increases. Our model is well-suited for realizing theseedge states in photonic waveguide lattices…