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We propose a simple two-dimensional acoustic crystal to realize topologicallyprotected edge states for acoustic waves. The acoustic crystal is composed of atriangular array of core-shell cylinders embedded in a water host. By utilizingthe point group symmetry of two doubly degenerate eigenstates at the \Gammapoint, we can construct pseudo-time-reversal symmetry as well as pseudo-spinstates in this classical system. We develop an effective Hamiltonian model forthe associated dispersion bands around the Brillouin zone center, and find theinherent link between the band inversion and the topological phase transition.With numerical simulations, we unambiguously demonstrate the unidirectionalpropagation of acoustic edge states along the interface between a topologicallynontrivial acoustic crystal and a trivial one, and the robustness of the edgestates against defects with sharp bends. Our work provides a new designparadigm for manipulating and transporting acoustic waves in a topologicallyprotected manner. Technological applications and devices based on our designare expected in various frequency ranges of interest, spanning from infrasoundto ultrasound.

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals