Metallic three-coordinated carbon networks with eight-membered rings showing high density of states at the Fermi level

Using a density functional method to study the electronic structure of various three-coordinated sp(2) carbon nanostructures, we find that the presence of an eight-membered ring adjoined to two five-membered rings in a unit cell brings about the simultaneous occurrence of flat and dispersive bands, quite similar to the band structure of precious metals. These bands are parts of an anisotropic Dirac cone tilted from an isotropic one. We reveal that in-phase and out-of-phase oscillations in the sign of the phase of the Kohn-Sham orbital contribute to the appearance of the unique band structures.