Double Dirac cones in two-dimensional photonic crystals with C6 symmetry

We analyse the double Dirac cones in two-dimensional photonic crystals with symmetry, which lack the reflection symmetry about six-fold axes of the triangular lattice. The double Dirac cones are constructed by accidental degeneracy of the and modes at the Brillouin zone center, which corresponds to the transition point between a trivial and a nontrivial topological phase. Based on the tight-binding approximation, the dispersion relation near the Brillouin zone center is analytically solved to give a pair of identical and isotropic cones, that is, the double Dirac cone. In particular, the double Dirac cones occur for both TM and TE modes in a complementary configuration of the photonic crystal consisting of triangular rods or holes as hexagonal clusters. The topological feature of the photonic crystal is manifest on the robust transport of helical edge states at the interface between two topologically distinct phases.