On-chip valley phononic crystal plates with graded topological interface

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 psi(BA) and psi(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.