Stokes and anti-Stokes Raman spectra of small-diameter isolated carbon nanotubes -: art. no. 115428

By measuring the anti-Stokes (AS) and Stokes (S) Raman spectra on the same isolated single-wall carbon nanotube (SWNT), we here determine the electronic transition energies E-ii experimentally (E-ii(exp)), and then we compare these E-ii(exp) with the E-ii values obtained with theoretical predictions (E-ii(cal)). In such an approach, the nanotube (n,m) structure identification depends on the theory parameters, but the experimental determination of E-ii(exp) does not, and depends only on the experimental AS/S intensity ratio and the laser energy E-laser used in the experiment. We measured the radial breathing mode frequency omega(RBM) and E-ii(exp) for specific tubes, and we then performed the (n,m) identification by using the d(t) diameter dependence of the electronic transitions. We present such an analysis for a wide nanotube diameter range, focusing primarily on small diameter SWNTs (d(t)<1.1 nm), where there are very few (n,m) possibilities for SWNTs that can be in resonance with the appropriate laser energy E-laser. This allows an experimental determination of E-ii(exp) values to be made for a variety of (n,m) SWNTs. Our experimental results indicate that: (i) the large curvature in small diameter tubes induces a sigma-pi hybridization, thus lowering the electronic band energies, and (ii) the simple formulation of the tight binding model (gamma(0)=2.89 eV) to determine E-ii starts to deviate from E-ii(exp) for tubes with d(t)<1.1 nm, but the deviation DeltaE(22)=E-22(exp)-E-22(cal) remains smaller than 20 meV for d(t)greater than or equal to0.83 nm. A comparison between E-ii(exp) data obtained from Raman and photoluminescence is made, and a comparison is also made between E-ii(exp) data for SWNTs and double-wall carbon nanotubes.