具有良好可重构性、良好缺陷兼容性及紧凑型的声学拓扑结构可能成为声学发展中一个有前景的方向.本文设计了一种可调谐、应用于空气声的二维宽带复合蜂窝形晶格结构,其元胞拥有两个变量:一个是中心圆的缩放参数s,另一个是"花瓣"图案围绕其质心的旋转角度q.研究发现当s为1.2, q为±33°时,在结构的布里渊区中心点出现四重简并态.在±33°两侧,能带会发生反转,体系经历拓扑相变;同时,结构的相对带隙宽带逐渐增加,其中q为0°和60°时,相对带宽分别为0.39和0.33.本研究还计算了由这两种转角的声子晶体组成的拼合结构的投影能带,发现在其体带隙中存在着边界态并验证了此拓扑边界的缺陷免疫特性.最后通过变化s,构建了一种非周期性双狄拉克锥型的声拓扑绝缘体并验证了其缺陷免疫性.本研究的体系相对带宽显著超过已知体系,将为利用声拓扑边界的声波器件微型化打下良好的基础.

The discovery of quantum Hall effect and quantum spin Hall effect has set off a new research upsurge in condensed matter physics. As is analogous to electronic systems, many novel optical and acoustic control devices have been designed by using the defects- immune and backscatter suppression of topological edges in photonic crystals and phononic crystals, which greatly enriches the current physical world and arouses more research enthusiasm. With the study of acoustic topological structure, it has been found that the realization of good reconfigurability, good compatibility against manufacturing defects, and compact acoustic topological insulators may become a promising development direction. This imposes higher requirements on the topological band gap width of the current acoustic topological structure. At the same time, the restriction on the using of the same primitive unit cells in previous researches does not reveal the implementation of aperiodic double Dirac cone topological insulators. Here in this work we present a tunable, two-dimensional broadband composite honeycomb lattice structure for airborne sound. Firstly, We construct a hexagonal structure and then take a circle with a radius of r(1) in the center. Then the circle is anisotropically scaled with the scaling factor s, which means that the x direction of the circle is expanded by times root s and the y direction is reduced by 1/root s times to form an ellipse. Then, we perform a translation and rotation transformation on the ellipse, and finally construct a "triangular-like" petal pattern at each vertex of the hexagon. Secondly, we place a circle with a radius of r(2) in the center to achieve the unit cell of the phononic crystal. This cell has two variables. One is the rotation angle theta of the petal pattern around its centroid, and the other is the scaling factor s. We find that there is a quadruple degenerate state at Gamma with s = 1.2 and theta = +/- 33 degrees. On both sides of +/- 33 degrees, changing theta will induce an inverted band and a topological phase transition. At the same time, the relative band gap of the structure increases gradually. When q is 0 degrees and 60 degrees, the structures are two topologically distinct broadband phononic crystals with relative band widths of 0.39 and 0.33, respectively. Calculated by the finite element software Comsol, the edge states existing in the band gap are found, and the backscattering immunity characteristics of the topological edges to defects such as right angle, Z-angle, disorder, and cavity are confirmed. For the first time we construct a aperiodic double Dirac cone acoustic topological insulators with different values of s and change their defect immunity. The research system is rich in function, and its relative bandwidth can even exceed 0.5 for a certain s value, which significantly exceeds the bandwidth of the known structure, and lays a good foundation for miniaturized acoustic wave devices taking full advantage of acoustic topological edges. Meanwhile, the realization of aperiodic topological insulators shows that the system can be used more flexibly for acoustic structure design.