Zak phase induced interface states in two-dimensional phononic crystals

Interface states have great practical applications, therefore, searching for the existence of interface states has both scientific significance and application prospects. In this work, we tilt the structure unite of two-dimensional phononic crystal with a square lattice to construct an oblique lattice possessing linear Dirac dispersion. The Dirac dispersion gives rise to a π jump of the Zak phases of the bulk bands, so that the projected band gaps at both sides of the Dirac cone have opposite signs of surface impedance, resulting in deterministic interface states at the interface formed by the phononic crystal with a square lattice and its tilted oblique lattice system.