Wu Huizhou, Wei Guochao, Liu Zhenzhen, Xiao Jun-Jun
Opt Lett. 2021 Sep 1;46(17):4256-4259. doi: 10.1364/OL.434306.
The square-root operation can generate systems with new (to the best of our knowledge) topological phases whose topological properties are inherited from the parent Hamiltonian. In this Letter, we introduce the concept of square-root topology in the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model and construct a square-root topological square nanoparticle lattice (SRTL) by inserting additional sites into the original 2D SSH model. We find that the topological states in the SRTL are intriguingly different from those in the corresponding SSH model (with on-site potential) due to the change in symmetrical characteristics. Plasmonic nanoparticle arrays are used to demonstrate this by including both nearest-neighbor and next-nearest-neighbor interactions within the dipole approximation. These unique topological states, such as the single corner mode and multiple topological edge modes, enrich the topological features produced by square-root operation and expand the scope to apply such topological features into photonic systems.
平方根运算能够生成具有新的（据我们所知）拓扑相的系统，其拓扑性质继承自母体哈密顿量。在本信函中，我们在二维（2D）Su-Schrieffer-Heeger（SSH）模型中引入平方根拓扑的概念，并通过在原始2D SSH模型中插入额外的位点来构建一个平方根拓扑方形纳米颗粒晶格（SRTL）。我们发现，由于对称特性的改变，SRTL中的拓扑态与相应的（具有在位势的）SSH模型中的拓扑态截然不同。通过在偶极近似内纳入最近邻和次近邻相互作用，利用等离子体纳米颗粒阵列对此进行了演示。这些独特的拓扑态，如单角模式和多个拓扑边缘模式，丰富了平方根运算产生的拓扑特征，并将此类拓扑特征应用于光子系统的范围得以扩展。
