Chirality-dependent environmental effects in photoluminescence of single-walled carbon nanotubes

The optical transition energies, $E_{11}$ and $E_{22}$, of single-walled carbon nanotubes (SWNTs) suspended in air have been investigated for 20 species by photoluminescence and excitation spectroscopies. We have studied the environmental effects in photoluminescence by comparing our results with those for the SWNTs wrapped by sodium-dodecyl-sulfate (SDS), as reported by Weisman and Bachilo [Nano Lett. 3, 1235 (2003)]. The energy differences between air-suspended and SDS-wrapped SWNTs, $\Delta E_{ii}=E_{ii}^{\text{air}}-E_{ii}^{\mathrm{SDS}}$, depends on the chiral vector $(n,m)$, specifically on the chiral angle and type of SWNT (type I or type II). The $\Delta E_{11}$ and $\Delta E_{22}$ mostly blueshifted, with the exception of the $\Delta E_{22}$ of some type II SWNTs (that have a small chiral angle), which redshifted. With an increase in the chiral angle, the $\Delta E_{11}$ increased in type I SWNTs and decreased in type II SWNTs. In contrast, the $\Delta E_{22}$ demonstrated opposite dependence on the chiral angle. The differences in $\Delta E_{11}$ and $\Delta E_{22}$ between type I and type II disappeared in the SWNTs with chiral angles close to 30° (near armchair). The $(n,m)$ dependence of the environmental effect on the transition energies can be explained by the difference in the effective mass, which contributes to the energy of Coulomb interactions between carriers.