Dirac cone in two- and three-dimensional metamaterials.

It is shown by analytical calculation based on the tight-binding approximation that the isotropic Dirac cone in the Brillouin zone center can be created in two- and three-dimensional periodic metamaterials by accidental degeneracy of two modes. In the case of two dimensions, the combination of a doubly degenerate E mode and a non-degenerate A1 mode of the square lattice of the C4v symmetry is examined. For three dimensions, the combination of a triply degenerate T1u mode and a non-degenerate A1g mode of the cubic lattice of the Oh symmetry is examined. The secular equation of the electromagnetic field is derived and solved with detailed analysis of electromagnetic transfer integrals by group theory. This is the first theoretical prediction of the presence of the Dirac cone in the three-dimensional periodic structure.