Broadband periodic and aperiodic acoustic topological insulator based on composite honeycomb structure
Authors: Pei Dong-Liang , Yang Tao , Chen Meng , Liu Yu , Xu Wen-Shuai , Zhang Man-Gong , Jiang Heng , Wang Yu-Ren ,   Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China,   University of Chinese Academy of Sciences, Beijing 100049, China,   Wuhan Second Ship Design and Research Institute, Hubei 430064, China
Published: December 2020

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 <i>r</i><sub>1</sub> in the center. Then the circle is anisotropically scaled with the scaling factor <i>s</i>, which means that the <i>x</i> direction of the circle is expanded by <inline-formula><tex-math id="M1">\begin{document}$\sqrt s $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20191454_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20191454_M1.png"/></alternatives></inline-formula> times, and the y direction is reduced by <inline-formula><tex-math id="M2">\begin{document}$1/\sqrt s $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20191454_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20191454_M2.png"/></alternatives></inline-formula> 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 <i>r</i><sub>2</sub> in the center to achieve the unit cell of the phononic crystal. This cell has two variables. One is the rotation angle <i>θ</i> of the petal pattern around its centroid, and the other is the scaling factor <i>s</i>. We find that there is a quadruple degenerate state at <i>Γ</i> with <i>s</i> = 1.2 and <i>θ</i> = ±33°. On both sides of ±33°, changing <i>θ</i> will induce an inverted band and a topological phase transition. At the same time, the relative band gap of the structure increases gradually. When <i>θ</i> is 0° and 60°, 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 <i>s</i> and change their defect immunity. The research system is rich in function, and its relative bandwidth can even exceed 0.5 for a certain <i>s</i> 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.