ENERGY-GAP OF ALTERNANT CARBON NANOTUBES

The energy spectra of two types of non-helical carbon nanotubes are investigated theoretically. It is shown that either the topological or the correlational contributions determine the width of the band gap. In some cases (for nanotubes with diameter <1 nm) the electron correlation changes qualitatively the results for the width of the energy gap Delta E: if in the one-electron approximation the band width Delta E = 0, the contribution of the electron correlation becomes dominant and increases the band gap Delta E > 0. At small diameter of the nanotubes (D < 1 nm) the ground state of the tubes corresponds to semiconductors with moderate or narrow energy gap, while at D > 1 nm Delta E decreases monotonously. The energy spectra of the planar ribbon polymers are compared with those of the iso-electronic nanotubes.