Conical dispersions induced interface states in two-dimensional photonic crystals

It is known that interface states are not guaranteed at the interface between two two-dimensional photonic crystals. To create an interface state, it is usual to decorate the structure near the interface. In this work, we construct a photonic crystal in an oblique lattice through tilting from a square lattice. Conical dispersion, existing in the oblique lattice, induces band inversion and results in two band gaps, separated by the projected band structure of it, possessing opposite signs of surface impedance. Therefore, interface states are guaranteed to exist at the interface between the square lattice and its “tilted” partner