Higher-order topological edge and corner states in C₃-symmetric phononic crystal plates

Higher-order topological insulators (HOTIs) have attracted much attention because of their topologically protected edge and corner states providing new ways to manipulate the robust propagation of elastic waves. However, once most elastic topological insulators are designed, the paths of their edge states cannot be changed and the valley-selective corner states depend on the different excitation frequencies, which may hinder the application of TIs. Here, we propose an elastic valley phononic crystal plate (PCP) with a rotatable cylindrical scatterer. The inversion symmetry of the C₃ system is broken by rotating cylindrical scatterers, realizing a topological phase transition and giving the flexibility of edge states and corner states. Simulation and experimental results indicate that elastic waves can only propagate along different interfacial paths and are robust to defects (cavities and disorder). In addition, the Wannier center theory predicts the location of corner states and can explain their valley selectivity well. The proposed elastic TIs combine the features of higher-order topology and valley degree of freedom, which provide references and methods for realizing multidimensional topological states and may contribute to their applications in the flexible regulation of elastic waves and energy harvesting.