Real and imaginary edge states in stacked Floquet honeycomb lattices

Alexander Fritzsche,Bastian Höckendorf,Andreas Alvermann,Holger Fehske

doi:10.1140/epjb/e2020-10233-0

Alexander Fritzsche, Bastian Höckendorf + Show 2 more

Open Access

https://doi.org/10.1140/epjb/e2020-10233-0

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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.Graphical abstract

Highlights

After their discovery in 1980 [1] topological states of matter have been in the focus of condensed matter research for the past decades and have led to fundamental insights regarding the interplay between bulk topology and edge transport [2,3,4]
In contrast to the counterpropagating edge states in real gaps, we find that the edge state in the imaginary gap remains localized during time evolution while its amplitude continuously increases
The stacked Floquet honeycomb model introduced in the present paper allows for the realization of two counterpropagating edge states in real gaps and a single edge state in an imaginary gap

Summary

Introduction

After their discovery in 1980 [1] topological states of matter have been in the focus of condensed matter research for the past decades and have led to fundamental insights regarding the interplay between bulk topology and edge transport [2,3,4]. In contrast to the counterpropagating edge states in real gaps, we find that the edge state in the imaginary gap remains localized during time evolution while its amplitude continuously increases. This amplification is protected by time-reversal symmetry. For this lattice configuration, the propagation of the edge states is investigated.

Stacked honeycomb model

Edge state propagation in a square lattice

Conclusion