一维颗粒声子晶体的拓扑相变及可调界面态

The topological phase transition and the tunable interface states in granular crystal

基于Su-Schrieffer-Heeger模型,构造了一种一维非线性声子晶体,通过调控外加在声子晶体上的预紧力,可调控声子晶体的拓扑态,从而实现拓扑相变.利用这一效应,把该非线性声子晶体与另一线性声子晶体形成异质结构,可以实现一种新型声学开关:通过调节预紧力即调控非线性声子晶体的拓扑相,可以实现异质结构中界面态从无到有的转变,从而实现了开关效应.利用该效应可望开发新型声学器件,如可调谐振器、可调滤波器、可调隔振器等.

Topological phase is a new degree of freedom to describe the state of matter in condensed matter physics. One could predict the existence of the interface state between two topological different phononic crystals. The band structures of phononic crystal depend on the characteristics of their composite and their combination, such as geometry, filling fraction,and stiffness. However, after the phononic crystal is fabricated out, it is relatively difficult to tune their band structure and its topology. In order to broaden the application scope of phononic crystals, different kinds of tunable phononic crystals have been proposed. One method to achieve this tunability is to introduce nonlinearity into the phononic crystals.Granular crystals is one type of tunable nonlinear material, whose nonlinearity stems from nonlinear Hertzian contact.By changing the static precompression, the dispersion of granular crystals can be tuned. In this paper, by combining topology with nonlinear we create a new type of interface state switch without changing the experimental setup. Based on the Su-Schrieffer-Heeger（SSH） model—an example of a one dimensional（1D） topological insulator, we present a 1D nonlinear granular crystal, to realize the topological transition by precompression. First, we construct a 1D mechanical structure, which is made up of nonlinear granular crystal and linear phononic crystal. The 1D nonlinear granular crystal is simplified as a ＂mass-spring＂ model with tunable elastic constant and invariable elastic constant. By calculating the band topology—the Zak phase, we found that the Zak phase of the two bands can switch from π to 0. There exist a critical precompression Fo, when F 〉F0 the Zak phase of the band is π, when F〈 Fo the Zak phase is 0. The granular crystal vary from nontrivial bandgap to trivial one as precompression gradually increase. This effect enables us to design interface state switch at the interface between granular crystals with trivial and nontrivial band gap. Furthermore,when F 〈F0, we find that the localization of interface state decreases as the applied precompression increases. Thus,we investigate existence of the interface state under different precompression and found that the interface state can be controlled freely. We anticipate these results to enable the creation of novel tunable acoustic devices.