In this work, we construct on-chip valley phononic crystal plates by building up triangular silicon pillars on the silicon plate. We introduce the graded interface sliding for two typical interfaces ψ_BA and ψ_AB, by modulating the horizontal lattice constant in a selected region in PC plate. Based on simulation and laser ultrasonic technique, we present the frequency range evolution of topological edge states from the gapless feature to gapped one. We demonstrate the displacement distribution of topological edge states in two graded interfaces, magnifying numerically the topological rainbow phenomena. In particular, we characterize the plate wave propagation through both types of graded interfaces, observe the abnormal refraction pattern behind the truncated interfaces, and underline abnormal refraction to the splitting of wave vector in PC plate. Our graded interfaces provide new clue to control elastic wave propagation based on valley degree of freedom.

在这项工作中，我们通过在硅板上构建三角形硅柱来构建片上谷声子晶体板。我们介绍了两个典型界面ψ _BA和ψ _{AB的渐变界面滑动}，通过调制 PC 板中选定区域的水平晶格常数。基于仿真和激光超声技术，我们展示了拓扑边缘状态从无间隙特征到有间隙特征的频率范围演变。我们展示了拓扑边缘态在两个渐变界面中的位移分布，在数值上放大了拓扑彩虹现象。特别地，我们描述了板波通过两种渐变界面的传播，观察了截断界面后面的异常折射模式，并强调了 PC 板中波矢量分裂的异常折射。我们的分级界面为基于谷自由度控制弹性波传播提供了新线索。