Double Dirac cones in triangular-lattice metamaterials

It is shown by tight-binding approximation and group theory that a double Dirac cone, or a pair of two identical Dirac cones, of the electromagnetic dispersion relation can be created in the Brillouin zone center by accidental degeneracy of E(1) and E(2) modes in triangular-lattice metamaterials of C(6v) symmetry. The Dirac point thus obtained is equivalent to a zero-index system, so we can expect unique optical propagation phenomena such as constant-phase waveguides and lenses of arbitrary shapes. Zitterbewegung is also expected without disturbance due to an auxiliary quadratic dispersion surface, which is present for other combinations of mode symmetries to materialize the Dirac cones. To the best of the author's knowledge, this is the first prediction of the presence of a double Dirac cone in metamaterials.