Three-dimensional photonic Dirac points stabilized by point group symmetry

We discover a pair of stable 3D Dirac points, 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nano-fabrication for visible-frequency photonic applications. The Dirac points carry nontrivial $Z_2$ topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the $C_6$ symmetry lead to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. {The Dirac points are characterized using ${\vec k}\cdot{\vec P}$ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splites the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.