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Valley topological States in double-surface periodic elastic phonon crystal plates

The topological insulators, as its novel physical properties, such as transmission protection, energy loss free and defect immunity, have generated much recent interest. It is necessary to introduce the concept of topology into elastic materials to enrich the research content of elastic waves. The concept of Valley State provides the simplest solution to realize topological states. In this paper, we design a double surface periodic phononic crystal based on elastic material, the upper and lower surfaces are composed of periodically arranged triangular prismatic scatterers. Valley topological states of elastic phononic crystals are observed when only focus on Lamb waves in out-of-plane mode by numerical simulation, we also analyze theoretically the valley Chern number, as the angle between the triangular prism and the positive direction of the X axis is greater than 0, the Chern number of K is 1/2, while the angle is less than 0, the Chern number is -1/2, K' has the opposite the Chern number. By simply tuning the geometry of the scatterer, the inversion of the energy band will occur and the topological phase transition will be realized. We find that the frequency of edge states in valley topology can be regulated by adjusting the height of scatterers. Moreover, wide frequency excitation is achieved at the edge interface composed of different valley Hall materials, which proves that the idea of adjustable edge state frequency can be implemented in elastic materials. Based on the two different valley phase phononic crystal, we studied the topological transport, it exhibited excellent transmission performance even the Z-shaped interface. we found that the design of double surface structure has stronger immune effect to defects than single surface, which achieves a new degree of freedom in the valley topology protection of elastic wave excitation.