Twist-projected two-dimensional acoustic topological insulators

Acoustic analogs of electronic or photonic topological insulators provide unique approaches to manipulate sound wave propagation. Inspired by twist-induced topological photonic insulators, here we propose a type of two-dimensional acoustic topological insulator (TI) via projecting a section of a three-dimensional twisting structure to a plane, assembling the projected meta-atoms into metamolecules, and arranging the metamolecules into unit cells to form a honeycomb lattice. It follows that in this acoustic TI, topological phases mimic pseudospin-up and pseudospin-down states, and the pseudospin-orbital couplings are tuned via changing the rotation angles of the meta-atoms, which eventually leads to band inversion. By calculating acoustic band structures, pressure field distributions, and spin Chern numbers of bands, we verify that the topological phase transition occurs around the double Dirac cone and present the topological phase diagram as a function of the rotation angle of the meta-atoms. Once the coupling between adjacent metamolecules is sufficiently strong, mode inversion of topological states emerges. Furthermore, we numerically demonstrate the existence of topologically protected edge states. It is shown that robust pseudospin-dependent one-way transmission is immune to defects at the edge of topological distinct regions, which can be applied to acoustic wave transmissions and communications. Our approach in acoustic systems provides a strategy to explore abundant topological states in two-dimensional systems.