High-frequency topological corner and edge states in elastic honeycomb plates

Abstract

Higher-order topological insulators (HOTIs) have attracted considerable attention because of their topological properties of low-dimensional topological corner states and edge states that exist in bandgaps. High-frequency edge states and corner states can be realized by controlling the interface configuration. However, most studies on HOTI focus on the bandgap at low frequencies, and the valley-selectivity of corner states is generally realized through a big-angle rotation. Here, we propose an elastic valley phononic crystal plate with an out-of-plane wide band gap to realize the edge states and corner states in the high-frequency bandgap. The sliding displacement of the resonators is tuned to control the topological phase transition. The rainbow trapping of topologically protected edge waves (TPEWs) is realized through the modulation of group velocities in the gradient structure based on the sliding parameter, and the valley-selectivity of corner states at high frequencies is further explored by engineering positions of the valley polarization. The simulation and experimental results indicate that TPEWs can be transmitted to different locations according to the switch of frequencies and corner states still hold valley-selectivity in high-frequency bandgaps. The proposed honeycomb plates provide generality for realizing high-frequency edge states and corner states and broaden the application for vibration transmission control and elastic energy trapping.