Abstract: Based on the quantum valley-hall effect,a two-dimensional valley phononic crystal topological insulator with C_3v symmetry has been designed.By rotating the angle of the scatterers inside the lattice,the topological properties of the lattice were changed.A supercell structure was constructed using two-dimensional valley phononic crystals with different topological phases,and the high-order topological corner states were investigated.The results show that when the rotation angle is changed,the symmetry of the system will decrease from C3v symmetry to C₃ symmetry.When -30°<θ< 0°,the system corresponds to a non-trivial phase,while when 0°<θ<30°,the system corresponds to a trivial phase.When the internal lattice has a non-trivial phase and the external lattice has a trivial phase,there are three continuous corner states at the corners of the Zigzag boundary of the supercell structure.However,when the internal lattice has a trivial phase and the external lattice has a non-trivial phase,there are no corner states in the supercell structure.Before and after introducing disorder defects,the intrinsic field distribution of the corner states shows no significant change,demonstrating good robustness.

Key words: topological insulator, phononic crystal, quantum valley-hall effect, corner state