Curvature effects on the E33 and E44 exciton transitions in semiconducting single-walled carbon nanotubes

The E33 and E44 optical transitions of small diameter (0.7-1.2 nm) semiconducting single-walled carbon nanotubes are probed using deep blue (415-465 nm) resonance Raman spectroscopy and photoluminescence excitation spectroscopy in the UV and blue regions (280-488 nm). Individual radial breathing mode features, as well as Raman and photoluminescence excitation maxima, are assigned to specific nanotube chiralities. The chiral angle dependence of Raman intensity within a given 2n+m branch is found to continue, as does the trend toward increased excitation linewidths and weaker Raman intensities as higher lying transitions are accessed. The semiconducting E33 and E44 transition energies obtained for the largest observed diameters confirm recent results that show that these transitions reside on a blueshifted scaling-law line, separate from that describing E11 and E22 behaviors. Energies for nanotubes with diameter less than 0.9 nm, however, are not explained by any previous scaling-law fits. This behavior at small diameters is interpreted in terms of both a crossing over of the E33 and E44 energy trend lines for a given 2n+m branch and a chirality dependence in the many-body exciton effects that becomes significant at high curvatures.