Double Dirac cones in two-dimensional phononic crystals.

By utilizing the accidental degeneracy of two double-degenerate Bloch eigenstates, a double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can be accurately predicted by the method from first-principles. A slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated.