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

中文翻译：

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堆叠的Floquet蜂窝格中的实边缘和虚边缘状态

摘要

我们提出了一个非Hermitian Floquet模型，该模型在真实和虚带隙中具有拓扑边缘状态。该模型利用了两个堆叠的蜂窝状晶格，这些晶格可以通过四种不同类型的非Hermitian时间反转对称性进行关联。实现正确的时间反转对称性可以为我们提供真实间隙中的两个反向传播的边缘状态，或虚构间隙中的单个边缘状态。反向传播的边缘状态允许沿晶格周长螺旋或手性传输。与之形成鲜明对比的是，我们发现假想间隙中的边缘状态不会传播。取而代之的是，它在空间上保持局部性，而其幅度不断增加。我们的模型非常适合在光子波导晶格中实现这些边缘状态。

图形概要