Tight-binding and k.p methods in carbon nanotubes: features, comparison and improvement

We use the tight-binding and the k→ · p→ methods to compute the energy dispersion relations and the density of states of carbon nanotubes, comparing the obtained results and pointing out the advantages and the drawbacks of the two techniques. We discuss a numerical method to easily obtain with the tight-binding technique only the most interesting energy bands, introducing an unusual but convenient choice of graphene unit vectors.