Theoretical and experimental demonstrations of the transversely symmetric and antisymmetric properties of topological edge states

Topological phononics are well known for their topological edge states (TES) due to backscattering immunity and pseudospin-dependent phonon transport. Here, we study two types of TES on valley phononic crystal (PC) plates. We magnify the transversely symmetric and antisymmetric properties by observing the displacement distribution in both simulations and experiments. We underline the theoretical origin of transversely symmetric and antisymmetric properties based on a simplified mass-spring model, i.e. the combination of the phase difference caused by the periodicity of the PC plate and the phase difference between sites p and q in the unit cell. Our results enrich the features of TES and offer the possibility of designing mechanical devices or controlling wave propagation along phonon circuits.