Geng Zhi-Guo, Peng Yu-Gui, Lv Huanzhao, Xiong Zhan, Chen Zhaojiang, Zhu Xue-Feng
College of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Republic of China.
School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China.
J Phys Condens Matter. 2021 Dec 21;34(10). doi: 10.1088/1361-648X/ac3f65.
The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal () direction. With the nontrivial intralayer couplings, the opened degeneracy at the-direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in thedirection. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.
高阶拓扑绝缘体的平方根衍生物是最近被提出的，其拓扑性质继承自平方哈密顿量。在此，我们通过在法线（）方向堆叠二维平方根晶格来呈现一种三维（3D）类平方根声子晶体。由于非平凡的层内耦合，在方向上打开的简并性诱导出多个声学局域模的出现，即扩展的二维表面态和一维棱边态，它们源自系统的平方根性质。类平方根高阶拓扑态可以通过选择性地去除边界处的空穴来进行调控和设计。我们进一步通过在每个平方根层上引入交错层间耦合，在三维声子晶体中提出了一种三阶拓扑角态，这导致在方向上出现非平凡的体极化。我们的工作为高维平方根拓扑材料提供了启示，并在设计具有声音捕获和声传感功能的先进功能器件方面具有潜力。
