Curvature Effects on Electron States of Semiconducting Nanotubes

Based on the generalized tight-binding model we study the electronic structure of all the semiconductor nanotubes with their diameters between 7.5 Å and 15.5 Å. We find that the van Hove peak separations versus nanotube diameters shows a qualitative difference from the well known plot based on zone-folding models. It has been clarified that the top of the valence band of the (n, m) nanotube in which the remainder of |n − m| divided 3 is 1 is lower in energy than that of the other semiconducting nanotubes of which remainder is 2. This dependence is originated from the wavefunction characters at the wavenumbers allowed by the periodic boundary condition along the circumference imposed on the hexagonal Brillouin zone of the graphene sheet.