Band-gap formation in (n,0) single-walled carbon nanotubes (n=9,12,15,18):: A first-principles study -: art. no. 073404

We study the electronic structure of the carbon nanotube theoretically by the first-principles techniques using the local-density approximation (LDA) with the many-body correction in the GW approximation. We find that the (9,0) tube is gapful irrespective of naive expectation from the graphene band structure. All of the pi-sigma hybridization effect, lattice relaxation effect, and many-body effect due to electron interaction enhance the band gap, and the value is as large as 0.17 eV when taking into account all effects. For the (n,0) nanotubes with n=9, 12, 15, and 18, the LDA gap is found to range from 0.08 to 0.02 eV. These sizable gap values obtained by the most reliable methods to date shed light on the classification of carbon nanotubes by their electronic transport properties.