Band theory and electronic structures of carbon nanotubes

A band structure model for carbon nanotubes taking into account the deformation potential characterizing the conformal mapping of graphene to tubules is presented and overlap is introduced in the π band calculations. This model corresponds to the study of a one-dimensional (1D) system and is not simply the limit of a 2D system becoming quasi-1D. While development is explicitly made for the zigzag tubules, the method itself can also be applied to the armchair and chiral configurations by modifying the structure factor and boundary conditions.