声学蜂窝结构中的拓扑角态

高阶拓扑绝缘体是近年来发现的一类具有特殊拓扑相的新型拓扑绝缘体,目前已在光学、声学等多种经典波系统中实现.本文采用数值模拟方法研究了一种二维声学蜂窝结构,通过调节胞内和胞间耦合波导管,使体能带发生反转诱导拓扑相变,进而利用拓扑相构建出声学二阶拓扑绝缘体.蜂窝结构的拓扑性质可以用量子化的四极矩Q_ij表征,当Q_ij=0时,系统是平庸的;而当Q_ij=1/2时,系统是拓扑的.基于该蜂窝结构,分别研究了六边形和三角形结构的声学高阶态,在两种构型的蜂窝结构中均观测到了孤立的零维角态,研究结果表明只有存在钝角的六边形结构对缺陷具有鲁棒性,受拓扑保护.本文的拓扑角态丰富了高阶拓扑绝缘体的研究,同时可为紧凑声学系统中的鲁棒限制声提供一条新途径.

Topological corner states in acoustic honeycomb structure

In recent years,a new type of topological insulator,termed higher-order topological insulator,has attracted tremendous research interest.Such exotic lower-dimensional topological boundary states have been extended and reproduced in classical systems,such as optics and acoustics.In this paper,a two-dimensional acoustic honeycomb structure with a triangle resonant cavity is numerically studied.Topological phase transition is induced by gradually adjusting the intracell and intercell coupling,and then the topological phase is used to construct a second-order topological insulator.The topological properties of second-order topological insulators can be characterized by using the quantized quadrupole moments.When quantized quadrupole Q_ij=0,the system is trivial,while Q_ij=1/2,the system is topologically nontrivial.We investigate the acoustical higherorder states of triangular and hexagonal structures,respectively.The gapped zero-dimensional corner states are observed in both structures,but the robustness properties of the corner states emerge only in the hexagonal structures but not in the triangular-shaped ones.The topological corner modes will offer a new way to robustly confine the sound in a compact acoustic system.