Quasiparticle band structure of carbon nanotubes

We study the electronic structure of carbon nanotubes theoretically by first-principles techniques. Geometry is optimized with the local-density approximation (LDA) in density functional theory, and many-body effects between electrons are taken into account within the $\mathrm{GW}$ approximation. We find that the (5,0) tube is metallic even at the $\mathrm{GW}$ level, being different from the tight-binding result. The (6,0) tube is also confirmed to be metallic. The $\mathrm{GW}$ correction to LDA is found to be small in metallic tubes. The (7,0) tube is semiconducting, in which the $\mathrm{GW}$ correction considerably increases the gap. On the other hand, the $\mathrm{GW}$ correction is small in graphene, suggesting that the density functional theory gives a reasonable description of large nanotubes.