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 the curved waveguide paths by disclinations in the C 3 symmetric valley acoustic crystals with the non-Euclidean geometries. 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 edge dislocation. Our work may provide a route to study new exotic phenomena related to topological defects in non-Euclidean geometries and metamaterials.