Energy spectrum and optical absorption spectra of carbon nanotubes with chiralities of (10, 10), (11, 9), and (12, 8)

Abstract

The energy spectra of single-wall carbon nanotubes (CNTs) with chiralities of (10, 10), (11, 9), and (12, 8) are calculated in the static fluctuation approximation for the Hubbard model. The choice of these systems for investigation was dictated by the fact that these systems are the most typical of heterogeneous samples obtained by synthesis. It is shown that in the chosen model and approximation, the type of conduction is independent of chirality, which contradicts the generally accepted opinion concerning the critical dependence of the CNT conduction current on the chirality indices. The optical absorption spectra of the CNTs under investigation are calculated using the resultant energy spectra. The shape of the optical absorption spectrum averaged over the known weight composition is in good agreement with experimental data. The results of investigation suggest that the rule according to which CNTs exhibit metal-type conductivity when the difference in the chirality indices is a multiple of three; otherwise, they have the semiconductor-type conductivity, is in all probability not general, but has applicability limits that can be established by rigorous calculations based on the Hubbard model.