Localization of edge state in acoustic topological insulators by curvature of space

Topological insulators (TIs) with robust boundary states against perturbations and disorders have boosted intense research in classical systems. In general, two-dimensional (2D) TIs are designed on a flat surface with special boundary to manipulate the wave propagation. In this work, we design a 2D curved acoustic TI by perforation on a curved rigid plate to localize the edge state by means of the geometric potential effect, which provide a unique approach for manipulating waves. We experimentally demonstrate that the topological edge state in the bulk gap is modulated by the curvature of space into a localized mode, and the corresponding pressure distributions are confined at the position with the maximal curvature. Moreover, we experimentally verify the localized edge state is still topologically protected by introducing defects near the localized position. To understand the underlying mechanism for the localization of the topological edge state, a tight-binding model considering the geometric potential effect is proposed. The interaction between the geometrical curvature and topology in the system provides a novel scheme for manipulating and trapping wave propagation along the boundary of curved TIs, thereby offering potential applications in flexible devices.