Geometric phase induced interface states in mutually inverted two-dimensional photonic crystals

The exposed surface of a truncated photonic crystal (PC) may or may not carry surface states. Likewise, when two PCs are joined together, there is no assurance that interface states can be found at the boundary. We show, however, that interface states must exist at the boundary between a two-dimensional dielectric PC and its "inverted" partner (the conjugate structure formed by interchanging the high/low dielectric region) as long as a common gap can be found above the lowest band and the crystal structures possess a mirror symmetry on average along the interface direction. The interface states form deterministically as a result of different geometric phases of the bulk bands across the boundary. As the existence is protected by topological principles, the interface state will persist even in the limit of extremely small common gaps. The presence of interface states is demonstrated theoretically for a variety of PCs and also experimentally.