Excitons in higher sub-bands of carbon nanotubes

International audienceIn this paper, we will present a brief review of linear and nonlinear optical properties of single-wall carbon nanotubes, with a special emphasis on the strong many body interactions responsible for the non-perturbative excitonic binding typical of one dimensional systems. These peculiar properties have several consequences such as efficient excitonexciton Auger annihilation [1] or anti-bunched single photon emission [2]. These effects are revealed in many experiments ranging from photo-luminescence to time-resolved transient absorption, on ensembles or at the single nanotube level. The excitonic nature of the lower energy transitions (the so-called S11 and S22 transitions) is now well established, for instance from two-photon photo-luminescence experiments [3]. The observation of side-bands in the absorption, PLE and luminescence spectra [4] are recognized as additional evidences of the excitonic character of these transitions. These side-bands are theoretically related to exciton-phonon bound states [5]. The origin of high-energy transitions (S33 and S44) was recently questioned in several works, on the basis that their energies follow a different scaling law than the first two ones [6]. It was therefore suggested that S33 and S44 transitions may not arise from excitons but rather from free carrier contributions [7]. We have performed Rayleigh scattering spectroscopy measurements on single suspended nanotubes in order to study the electronic resonances on a wide spectral range [8]. We report on the quasi-systematic observation of well defined phonon side-bands in the Rayleigh spectra of S33 and S44 transitions in structurally assigned S-SWNTs. This observation together with a careful lineshape analysis validates an excitonic description of optical excitations even for high-order transitions that couple to the continuum of lower bands. We show that the line-width remains compatible with the predicted exciton binding energy, which explains its surprising stability. We further investigate the case of M-SWNTs, which show an ambivalent signature. Rayleigh profiles are fairly well described by an excitonic lineshape, whereas the phonon side-bands, if observable, are much weaker. This is in agreement with the partial excitonic character of optical transitions in metallic nanotubes. [1] F. Wang et al., Phys. Rev. B 70, 241403 (2004) [2] A. Hogele et al., Phys. Rev. Lett. 100, 217401 (2008) [3] F. Wang et al., Science 308, 838 (2005) [4] F. Plentz et al., Phys. Rev. Lett. 95, 247401 (2005) ; O. Torrens, Phys. Rev. Lett. 101, 157401 (2008) [5] V. Perebeinos et al., Phys. Rev. Lett. 94, 027402 (2005) [6] C. Kane et al., Phys. Rev. Lett. 93, 197402 (2004) [7] P. Araujo et al., Phys. Rev. Lett. 98, 067401 (2007) ; T. Michel et al. Phys. Rev. B 75, 155432 (200