Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18): A first-principles study

Abstract

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 $\pi \text{−}\sigma$ hybridization effect, lattice relaxation effect, and many-body effect due to electron interaction enhance the band gap, and the value is as large as $0.17\mathrm{eV}$ 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 $0.08\text{to}0.02\mathrm{eV}$. 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.