Spiro-graphene: A two-dimensional metallic carbon allotrope of fused pentagons

Using density functional theory with the generalized gradient approximation, we explored the geometric and electronic structure of polymerized spiro [4,4]nonatetraene (spiro-graphene) as a possible two-dimensional carbon allotrope comprising sp2 and sp3 C atoms. By reflecting a shape of the hydrocarbon molecule, this two-dimensional allotrope has a covalent network of fused pentagons with nanometer-scale structural rippling. The covalent network is thermally and dynamically stable with a relatively high total energy, higher than graphene by 0.6 eV/atom. The spiro-graphene is a metal where two linear dispersion bands cross each other at the Fermi level. In addition to these linear dispersion bands, the covalent network possesses the Dirac nodal line just above the Fermi level and along the Brillouin zone boundary. Accordingly, the ribbons with zigzag edges derived from spiro-graphene possess edge states like those of graphene nanoribbons with zigzag edges.