Regular Article

Real and imaginary edge states in stacked Floquet honeycomb lattices

¹ Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
² Institut für Physik, Universität Greifswald, Felix-Hausdorff-Str. 6, 17489 Greifswald, Germany

^a e-mail: alexander.fritzsche@physik.uni-wuerzburg.de

Received: 5 May 2020
Received in final form: 17 June 2020
Published online: 5 August 2020

Abstract

We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with 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 remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices.