Hybridization effects and metallicity in small radius carbon nanotubes

Hybridization of the ${\mathrm{\sigma }}^{\mathrm{*}}$ and ${\mathrm{\pi }}^{\mathrm{*}}$ states of the graphene network is shown to be as important as band-folding effects in determining the metallicity of small radius carbon nanotubes. Using detailed plane-wave ab initio pseudopotential local density functional (LDA) calculations, we find that the electronic properties of small tubes are significantly altered from those obtained in previous tight-binding calculations. Strongly modified low-lying conduction band states are introduced into the band gap of insulating tubes because of strong ${\mathrm{\sigma }}^{\mathrm{*}\mathrm{-}}$ ${\mathrm{\pi }}^{\mathrm{*}}$ hybridization. As a result, the LDA gaps of some tubes are lowered by more than 50%, and a tube previously predicted to be semiconducting is shown to be metallic.