[论文解读] Observation of second-order topological insulators in sonic crystals

Xiujuan Zhang, Hai‐Xiao Wang+6 more|arXiv (Cornell University)|Jun 26, 2018

Topological Materials and Phenomena参考文献 47被引用 115

一句话总结

该论文在二维声学晶体中预测并实验性地演示了声学二阶拓扑绝缘体（SOTIs），显示有带隙的边界态和带隙内的角态，可通过超原子单元的角度调谐。

ABSTRACT

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization of generalized Berry phases of the bulk energy bands through the bulk-edge correspondence, a paradigm that can also be extended to acoustic and photonic systems. Recently, high-order topological insulators (HOTIs) are proposed and observed, where the bulk topological invariants result in gapped edge states and in-gap corner or hinge states, going beyond the conventional bulk-edge correspondence. However, the existing studies on HOTIs are restricted to tight-binding models which cannot describe the energy bands of conventional sonic/photonic crystals that are due to multiple Bragg scatterings. Here, we report theoretical prediction and experimental observation of acoustic second-order topological insulators (SOTI) in two-dimensional (2D) sonic crystals (SCs) beyond the tight-binding picture. We observe gapped edge states and degenerate in-gap corner states which manifest bulk-edge correspondence in a hierarchy of dimensions. Moreover, topological transitions in both the bulk and edge states can be realized by tuning the angle of the meta-atoms in each unit-cell, leading to various conversion among bulk, edge and corner states. The emergent properties of the acoustic SOTIs open up a new route for topological designs of robust localized acoustic modes as well as topological transfer of acoustic energy between 2D, 1D and 0D modes.

研究动机与目标

• 在声学系统中激发并实现第二阶拓扑绝缘体（SOTIs），超越紧束缚限制。
• 展示一个承载带隙边界态和带隙内角态的二维 sonic crystal，展示体—边—角的层级关系。
• 表明通过调节单元胞元原子的角度可以驱动影响体态、边态和角态的拓扑转变。
• 探索鲁棒性及在二维/一维/零维模态之间实现声学能量转移的潜力。

提出的方法

• 在超越紧束缚图像的二维 sonic crystals 中理论预测 SOTI 相。
• 在实验上实现所提出的二维 sonic crystal 并测量边界态和角态的光谱。
• 使用每个单元胞内元原子的角度作为调谐参数以诱导体态和边界态的转变。
• 将带隙边界态和带隙内简并的角态识别为体—边—角对应关系的标志。
• 通过改变几何参数来演示拓扑转变，使体、边、角态之间实现转换。

实验结果

研究问题

• RQ1 二维 sonic crystals 能否承载超越 tight-binding 模型的第二阶拓扑绝缘体相？
• RQ2 在声学系统中，体态、边态和角态是否呈现所预测的带隙边界态和带隙内角态？
• RQ3 通过调节元原子角度来驱动拓扑转变，使体、边和角态的特性重新配置？
• RQ4 是否有可能在该平台上实现鲁棒的局部化声学模态并在二维/一维/零维模态之间实现能量的受控转移？

主要发现

• 在二维 sonic crystal 中观察到带隙边界态。
• 观察到带隙内简并的角态。
• 实验实现符合超越紧束缚的理论预测。
• 通过调节单元胞元原子角度即可实现拓扑转变。
• 证明了体–边–角层级结构，能够实现鲁棒的局部化声学模态并在维度 2D/1D/0D 之间传递能量。