Electronic Band Structure of Carbon Nanotubes with Kekule Structure

Electronic band structure of carbon nanotubes with the Kekule structure is studied by the tight-binding approximation. We give a complete geometrical approach to structural properties of carbon nanotubes with bond alternation, including chiral and achiral tubes. When the Kekule is introduced, all carbon nanotubes become semiconducting with a small band gap at the Fermi level. The band gap of the carbon nanotubes depends only on the difference between C–C bond lengths or the resonance integrals.