Electronic structure and interband transitions of metallic carbon nanotubes

Abstract

Band structure of the metallic (n,n) carbon nanotubes (coefficients n are the indices of the two-dimensional primitive lattice vectors of the graphene lattice) is calculated in terms of a linear augmented cylindrical wave method. The results are used to correlate the minimum direct energy gaps E11 between the conduction and valence band singularities with the nanotube diameter d and optical absorption spectra. Significant deviations from the equation E11∼d−1 are observed. The ππ* gap energy increases monotonically with 1/d, whereas the σπ* gap width shows a minimum at n=10. In the (3, 3) tube, the conduction band singularity coincides with the Fermi level, resulting in a drastic increase of the density of states on this level.