Geometric phase and band inversion in periodic acoustic systems

The geometric-phase concept has far-reaching implications in many branches of physics(1-14). The geometric phase that specifically characterizes the topological property of bulk bands in one-dimensional periodic systems is known as the Zak phase(15,16). Recently, it has been found that topological notions can also characterize the topological phase of mechanical isostatic lattices(13). Here, we present a theoretical framework and two experimental methods to determine the Zak phase in a periodic acoustic system. We constructed a phononic crystal with a topological transition point in the acoustic band structure where the band inverts and the Zak phase in the bulk band changes following a shift in system parameters. As a consequence, the topological characteristics of the bandgap change and interface states form at the boundary separating two phononic crystals having different bandgap topological characteristics. Such acoustic interface states with large sound intensity enhancement are observed at the phononic crystal interfaces.