Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
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DOI：
10.1103/physrevb.102.125144
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发表时间：
2020-03
影响因子：
3.7
通讯作者：
Zhan Xiong;Zhi-Kang Lin;Hai-Xiao Wang;Xiujuan Zhang;Ming-Hui Lu;Yan-Feng Chen;Jian‐Hua Jiang
中科院分区：
文献类型：
--
作者：
Zhan Xiong;Zhi-Kang Lin;Hai-Xiao Wang;Xiujuan Zhang;Ming-Hui Lu;Yan-Feng Chen;Jian‐Hua Jiang
研究了具有反转对称性的宏观二维声子晶体，揭示了经典波系中的高阶拓扑物理。通过调整单个几何参数，可以同时控制主体和边缘的带状拓扑。体带隙形成了具有边缘状态的拓扑晶体绝缘体的声学模拟，边缘状态由于边缘的对称性降低而被带隙。在镜像对称性存在的情况下，边态的能带拓扑可以用Zak相来描述，这说明了高阶拓扑现象的关键特征--维度层次的能带拓扑。此外，边缘带在没有关闭体带隙的情况下经历了拓扑跃迁，揭示了体带和边带丰富的拓扑物理。我们在布里渊区使用对称性指示符来表征高阶拓扑带，并将对称性指示符与角电荷-角拓扑指数联系起来。这种方法使我们能够通过Bloch带的对称性来识别高阶拓扑边界态。然后，我们将反转对称性所保护的高阶拓扑现象推广到具有非对称对称性的拱形声子晶体，其中揭示了相似但略有不同的拓扑现象。在这些系统中，通过调节声学超材料的几何形状，可以利用丰富的多维拓扑跃迁在0D(角)、1D(边)和2D(体)声模之间进行拓扑转换。
Macroscopic two-dimensional (2D) sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is the key feature of higher-order topological phenomena. Moreover, the edge bands undergo topological transitions without closing the bulk band gap, revealing rich topological physics in both the bulk and edges. We characterize the higher-order topological bands using symmetry indicators in the Brillouin zone and link the symmetry indicators with the corner charge---a corner topological index. This approach allows us to identify higher-order topological boundary states through symmetry properties of the Bloch bands. We then generalize the higher-order topological phenomena protected by the inversion symmetry to arch-shaped sonic crystals with nonsymmorphic symmetries where similar but slightly different topological phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among 0D (corner), 1D (edge), and 2D (bulk) acoustic modes by tuning the geometry of acoustic metamaterials.