Absorption-spectral features of single-walled carbon nanotubes

We present a visual, intuitive connection between optical absorption line shapes and the underlying carbon nanotube structures. Within the tight-binding model, the absorption spectra can be linked directly to plots of energy contours and transition dipoles of a graphene sheet. Via two additional approaches, spectral features are shown only slightly altered by electronic correlations and σ–π orbital rehybridization. Despite dependence of electronic structures on chiral angles, it is proved that, if the tube diameter D is greater than the C–C bond length a, the absorption spectra are determined by D to the lowest order in a/D.