Tunable second-order elastic topological insulator and multi-dimensional rainbow trapping in ferroelectric phononic crystal plates

Abstract

Manipulation of elastic waves to achieve rainbow trapping effect has attracted wide attention. However, most of the current researches achieve rainbow trapping effect by changing the structural parameters, which means that the structure and mechanical properties are always fixed. Realizing the actively tunable working frequency range in elastic topological systems and obtain multi-dimensional rainbow trapping is still a challenge. In this paper, we design a topologically protected second-order thermostatic phononic crystal (PC) plate by using ferroelectric ceramic materials. By adjusting the rotation angle of the T-shaped scatterer, we can realize the multi-dimensional topological phase transition between the bulk and edge bands of elastic wave. Then, a “trivial-nontrivial-trivial” (TNT) heterostructure is constructed to obtain the coupled topological edge states of elastic wave, and the influence of intermediate coupling layer number on the edge states is investigated, which exhibits a multi-mode interference effect. Furthermore, the tunable topological edge states and corner states of elastic wave are obtained based on the temperature control of the ferroelectric materials. In addition, by employing the active tunability of the coupled edge states and corner states, the multi-dimensional topological rainbow trapping of elastic wave in ferroelectric PC plates is demonstrated. The edge and corner states of different frequencies are well separated and captured in different spatial positions, and the working frequency range of the PC plate can be easily tuned by controlling the temperature. Our results further promote the practical integration application of tunable and multi-dimensional elastic wave devices.