Tailoring the surface and interface states in a three-dimensional fragile topological insulator with kagome lattice

Abstract

Topological insulators, which are insulating in the bulk and conducting on the surface, have attracted great interest in recent years. The recently discovered topological surface and hinge states in three dimensions have provided promising methods for wave manipulation in classical systems. However, the combination of surface states and interface states has yet to be achieved in phononic crystals due to the missing topological surface states. Here, we experimentally demonstrate a fragile topological insulator with a bilayer kagome lattice. We observe the surface states in three different orientations and interface states formed by inversion of layer pseudospin sectors or bands. The combination of surface and interface states is investigated in $\mathsf{X}$-shaped waveguides. Our work may provide a platform for exploring unique acoustic applications based on surface or interface states.