Square-Root Higher-Order Topology in Rectangular-Lattice Acoustic Metamaterials

Square-root topology offers a distinctive scheme towards topological phases with unconventional spectral properties. In many cases, the formation of square-root topology is governed by the inherent lattice symmetry, with honeycomb lattices being prominent examples. Here, we report on the experimental discovery of square-root higher-order topological insulator phases in an acoustic metamaterial with decorated rectangular lattice. Through acoustic pump-probe techniques, we explore the boundary-dependent topological edge and corner states in both the parent and square-root acoustic metamaterials. We further validate their higher-order topologies as well as their spectral connections via various simulations. Our work not only substantiates the square-root higher-order topology in rectangular-lattice systems from the experimental aspect, but also serves as a step towards versatile higher-order topological phenomena in photonic, acoustic, and mechanical metamaterials.