Excitons and high-order optical transitions in individual carbon nanotubes: A Rayleigh scattering spectroscopy study

We examine the excitonic nature of high-lying optical transitions in single-walled carbon nanotubes by means of Rayleigh scattering spectroscopy. A careful analysis of the principal transitions of individual semiconducting and metallic nanotubes reveals that in both cases the line shape is consistent with an excitonic model, but not one of free carriers. For semiconducting species, sidebands are observed at $\sim 200\text{meV}$ above the third and fourth optical transitions. These features are ascribed to exciton-phonon bound states. Such sidebands are not apparent for metallic nanotubes, as expected from the reduced strength of excitonic interactions in these systems.

Figure 1

(Color online) (a)–(d) Rayleigh scattering spectra of individual suspended $S\text{-SWNTs}$ $\left\{\left[\text{mod}\left(n-m\right),3\right]=1,2\right\}$ with increasing diameters. The scattering intensities have been normalized by the cube of the photon energy. The vertical dotted lines highlight the $\sim 200\text{meV}$ blueshifted phonon sidebands. The stars in the Rayleigh spectra (a) and (b) indicate the laser energy for the Raman measurements. (e)–(h) Raman data for a (12,10) and a (16,12) SWNT. The RBM frequencies of (e) $163{\text{cm}}^{-1}$ and (h) $130{\text{cm}}^{-1}$ yield diameters of 1.50 and 1.98 nm, respectively (Ref. 18). The semiconducting nature of the nanotube is further confirmed by the narrow and bimodal Raman $G$ feature (Ref. 19). The Raman spectra have been fit to Lorentzian profiles. (i) Close-up of the PSB associated with the $S_{44}$ line for 3 different SWNTs. The spectra have been shifted horizontally and normalized for clarity.

Figure 2

(Color online) Rayleigh scattering spectra for the $S_{33}$ transition of a (15,14) semiconducting nanotube (open circles) (a) and for the $M_{22}^{-}$ transition of a (27,12) metallic nanotube (b). Best fit of the profile to the free carrier (blue dashed line) and excitonic (red solid line) models. In both cases the excitonic model is more appropriate.

Figure 3

(Color online) (a)–(c) Rayleigh scattering spectra of individual suspended $M\text{-SWNTs}$ $\left\{\left[\text{mod}\left(n-m\right),3\right]=0\right\}$. The insets show details of the spectra near the expected positions of phonon sidebands (dotted lines). The stars in the Rayleigh spectra (a)–(c) indicate the laser energy for the Raman measurements. (d)–(h) Raman data. The RBM frequencies of (d) $106{\text{cm}}^{-1}$ and (g) $101{\text{cm}}^{-1}$ yield diameters of 2.60 and 2.75 nm, respectively (Ref. 18). (e), (f), and (h) $G$-mode spectra showing chirality dependent electron-phonon coupling, as expected for chiral metallic nanotubes (Ref. 20). Spectra in (d), (e), and (g) are fit to Lorentzian profiles, while the fits in (f) and (h) are based on Fano profiles.