Effective-mass theory of electron correlations in band structure of semiconducting carbon nanotubes

The band gap, the single-particle energy, and the effective mass are calculated for semiconducting carbon nanotubes in a random-phase approximation within a k . p scheme. The energy gaps are shown to be strongly enhanced due to the Coulomb interaction, while effects on the effective mass along the axis direction are small. For realistic values of the interaction parameter, effects of the dynamical screening are sufficiently weak, and the conventional screened Hartree-Fock approximation is shown to work quite well. Further, the band gap contains a term with a residual logarithmic dependence on the tube diameter d after being scaled by 1/d.