Résumé
By combining, on the same freestanding single-walled carbon nanotubes, electron diffraction and Raman experiments we have been able to answer several questions: 1- The radial breathing mode frequency (RBM) vs diameter relationship was derived for tube in the 1.4-3 nm diameter range without any modelization of nanotube electronic or mechanical properties. These results showed that the RBM vs diameter relationship was not simply inversely proportional to the nanotube diameter [1]. The role of the environmental conditions on the radial breathing mode frequency was also discussed. 2- The dependence of the frequency of the tangential modes (LO and TO) with the diameter of semiconducting tubes was found and compared with the predictions of different models [2]. 3- The comparison between incident excitation energies, for which an intense Raman signal was observed, and the calculated transition energies [3] allowed us to determine the values of the optical transition energies EM11, ES33 and ES44 for SWNTs in the 1.3-2.4 nm diameter range [2]. 4-These latter results question the origin of the correction, usually considered as related to the electron-electron correlation and exciton binding energy, the so-called Kane and Mele correction (Kane and Mele. Phys. Rev. Lett. 93, (2004), 197402), to explain the differences between the experimental and calculated transition energies. For semiconducting tubes, our experimental findings suggest that the exciton binding is very small or missing for the higher transitions ES33 and ES44, contrary to the lower transitions ES11 and ES22 [4]. [1] J.C. Meyer et al., Phys. Rev. Lett. 95, 217401 (2005) [2] M. Paillet, et al.,Phys. Rev. Lett. 96, 257401 (2006) [3] V. Popov and L. Henrard, Phys. Rev. B 70, 115407 (2004) [4] T. Michel, Phys. Rev. B (submitted)