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

The optical transition energies, E₁₁ and E₂₂, 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, ΔEᵢᵢ=Eᵢᵢᵃⁱʳ-EᵢᵢSDS, depends on the chiral vector $(n,m)$, specifically on the chiral angle and type of SWNT (type I or type II). The ΔE₁₁ and ΔE₂₂ mostly blueshifted, with the exception of the ΔE₂₂ of some type II SWNTs (that have a small chiral angle), which redshifted. With an increase in the chiral angle, the ΔE₁₁ increased in type I SWNTs and decreased in type II SWNTs. In contrast, the ΔE₂₂ demonstrated opposite dependence on the chiral angle. The differences in ΔE₁₁ and ΔE₂₂ 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.