Pseudospins and topological edge states in elastic shear waves

We present a new framework to realize topological edge states in elastic shear waves in a two-dimensional (2D) phononic crystal (PC). The PC has a simple structure and is composed of a triangular array of core-shell cylinders embedded in an epoxy background. By tuning the geometrical parameters of the cylinders, band inversion between E1 and E2 eigenstates can be achieved at the Brillouin zone (BZ) center, which signifies a topological phase transition from a trivial PC to a nontrivial PC. An effective Hamiltonian is developed to characterize the topology of the PC around the Γ point, and spin Chern numbers are identified as the appropriate topological invariant. Helical edge states are formed at the interface between topologically distinct PCs, and these edge modes exhibit interesting one-way propagation behaviors with little backscattering. With full-wave simulations, we unambiguously demonstrate the robustness of the edge states against different types of defects, which is due to the nontrivial topology of the system. These unidirectional and robust transport phenomena of elastic shear wave thus offer people a new degree of freedom to control and manipulating elastic waves and are expected to find potential applications in diverse fields.