Dirac cone and double zero materials

Materials with zero permittivity and zero permeability (double zero) possess very interesting wave manipulation characteristics. Systems with Dirac cones in the band structure also possess amazing wave transport properties. These two classes of material are actually related to each other. We show that dielectric photonic crystals can be designed and fabricated which exhibit Dirac cones at k = 0 at a finite frequency. A subset of such materials behave as if they have zero permittivity and zero permeability at the Dirac point, as well as exhibiting properties intrinsic to a Dirac cone.