Topologically protected zero-directional refraction of elastic waves in a pillared phononic crystal plate

Zero-directional refraction phenomenon refers to the capability where waves do not undergo refraction at a material interface under specific conditions, which has broad potential applications, particularly in the fields of optics, acoustics, and phononics. Previous research of zero-directional refraction rely on the zero or equivalent-zero index of the material parameters, which is quite challenging to manipulate the zero-directional transport of waves. In this paper, based on the topological theory, we have constructed a pillared phononic crystal (PnC) plate structure with pseudospin topologically protected transport, enabling zero-directional refraction of elastic waves without using zero or equivalent-zero index of the material parameters. By initially adjusting the contraction and expansion of the pillared unit cell, a band inversion effect between pseudospin dipoles and quadrupoles is induced, thus leading to a topological phase transition of elastic wave. Combining the phase matching between topological interface and terminal medias, the elastic waves in pillared PnC plate can exhibit zero-directional refraction behavior. Finally, it was demonstrated that the phenomenon of zero-directional refraction exhibits robustness in the presence of cavities and bends, and different incident angles. This research result provides new insights for designing and manipulating the emission and directional antennas of elastic waves.