Acoustic Metamaterial Realization of an Obstructed Atomic Insulator

The obstructed atomic insulator (OAI) is a newly proposed crystalline phase of matter whose electronic wavefunctions are not localized on individual lattice sites. These wavefunctions give rise to in-gap edge states that depend on the exact surface termination of the lattice. Here we realize an OAI analog in an acoustic metamaterial composed of a two-dimensional arrangement of air cavities and channels in a solid matrix. We extend the standard kagome structure by inserting an additional lattice site between each hexagon. The new 14-site unit cell lifts the degeneracy of the flat band at the Gamma point, transitioning the system into an acoustic OAI phase. We confirm the new phase by "imaging" the pressure wavefunctions using a local microphone in each lattice site. Our experimental observation confirms the existence of this previously theoretical OAI phase. More generally, we demonstrate a framework to use acoustic metamaterials for fast prototyping of exotic crystalline phases of matter.