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

Abstract

The topological insulator, as its novel physical properties, such as transmission protection, energy loss free and defect immunity, has aroused much interest recently. It is necessary to introduce the concept of topology into elastic materials to enrich the research contents of elastic waves. The concept of valley state provides a simplest solution to realize topological states. In this work, 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 only when focusing 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 <i>X</i> axis is greater than 0, the Chern number of <i>K</i> is 1/2; when the angle is less than 0, the Chern number is –1/2 . The <i>K</i> has the number opposite to 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 state in valley topology can be regulated by adjusting the heights 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. According to the two different valley phase phononic crystals, we study the topological transport, exhibiting excellent transmission performance, even the Z-shaped interface. We find that the designed double surface structure has a stronger immune effect to defects than single surface, achieving a new degree of freedom in the valley topology protection of elastic wave excitation.