Corrugation-induced metal-semiconductor transition in single-wall carbon nanotubes with a small radius

Armchair single-wall carbon nanotubes (SWCNTs) are theoretically predicted to be metallic in the simple zone-folding scheme and protected from the curvature effects. They are, however, found to be small-gap semiconductors, experimentally. Lacking the genuine band-gap opening mechanism for armchair SWCNTs, the Mott insulator concept was proposed previously for the nominally metallic carbon nanotubes. Using the ab initio local density approximation method, we show, in this paper, that the carbon nanotubes without corrugation are, in fact, not metastable. The corrugated structures are always lower in energy than those without corrugation. The size of corrugation increases rapidly with the nanotubes' curvature and vanishes for flat graphene. The corrugation breaks the local symmetry between two types of carbon sites, and a true band gap starts to develop once graphene sheets are rolled up into nanotubes.