ENERGY-GAP OF ALTERNANT CARBON NANOTUBES

The energy spectra of two types of non-helical carbon nanotubes are in vestigated theoretically. It is shown that either the topological or t he correlational contributions determine the width of the band gap. In some cases (for nanotubes with diameter <1 nm) the electron correlati on changes qualitatively the results for the width of the energy gap D elta E: if in the one-electron approximation the band width Delta E = 0, the contribution of the electron correlation becomes dominant and i ncreases 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 decreas es monotonously. The energy spectra of the planar ribbon polymers are compared with those of the iso-electronic nanotubes.