Real and imaginary edge states in stacked Floquet honeycomb lattices

TL;DR

This paper introduces a non-Hermitian Floquet model with stacked honeycomb lattices that exhibits topological edge states in both real and imaginary band gaps, revealing novel localized and propagating behaviors.

Contribution

The study demonstrates how different non-Hermitian time-reversal symmetries lead to distinct edge state phenomena in Floquet honeycomb lattices, including localized states with increasing amplitude.

Findings

Counterpropagating edge states in real gaps enable helical or chiral transport.

Edge states in imaginary gaps are localized and non-propagating, with increasing amplitude.

The model is applicable to photonic waveguide lattice implementations.

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.