Observation of triple-branch valley topological edge states and abnormal refraction in elastic phononic crystal plates

Topological edge states (TES) have attracted wide interest in elastic waves, due to its backscattering immunity and directional wave transportation. In this work, the triple-branch TES and their rich refraction behaviors are investigated in one single valley chiral phononic crystal (PC) plate with double-sided symmetric pillars. The triple-branch TES emerge simultaneously in one structure, and their robust transportation against disorder, cavity, and sharp bends are demonstrated in both simulation and experiment. Furthermore, the refraction be-haviors for triple-branch TES from PC plate into bare plate are unveiled both theoretically and experimentally, leading to the normal refraction for first branch TES while the abnormal refraction for the second or third branch TES. These results offer opportunity for designing mechanical device or controlling the wave propagation along phonon circuits in multiple bandwidths and with robustness.