Alignment defects in zigzag and armchair carbon nanotubules

Forming a carbon cylinder by rolling a sheet of graphite causes alignment defects of orbitals with a consequent change of the total elastic energy. Using a Green's function technique and total-energy minimalization of the one-dimensional unit cell, we obtain analytic expressions for the deformation potential energy and the densities of states. The calculated elastic coupling constants allow us to evaluate the gaps which are in good agreement with experimental values.