Defect-controlled topological edge states in the curved acoustic lattices

Abstract The concept of disclinations and dislocations, which are related to the real-space topology, have been widely studied in crystal materials. In two-dimensional (2D) materials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries. However, such geometries have not been linked to the effects of topological edge states. Here we construct two curved lattices in the C3 symmetric valley acoustic crystals by removing or inserting a wedge of the crystal, which correspond exactly to the conic and hyperbolic lattices. We then discuss the topological edge states as well as the curved waveguide modes in different defect-constructed structures. Simulation results show that the topological waveguide modes can be controlled not only by the alignment of topologically different valley acoustic crystals, but also by the 5|7 edge dislocation. Our work may provide a route to study new exotic phenomena related to topological defects in 3D non-Euclidean geometries.