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 Eiiexperimentally(Eiiexp), and then we compare these Eiiexpwith theEiivalues obtained with theoretical predictions (Eiical) In such an approach, the nanotube(n, m)structure identification depends on the theory parameters, but the experimental determination of Eiiexpdoes not, and depends only on the experimental AS/S intensity ratio and the laser energy ELaserused in the experiment. We measured the radial breathing mode frequency ωRBMandEiiexpfor specific tubes, and we then performed the (n, m)identification by using the dtdiameter dependence of the electronic transitions. We present such an analysis for a wide nanotube diameter range, focusing primarily on small diameter SWNTs (dt < 1.1nm), where there are very few(n, m)possibilities for SWNTs that can be in resonance with the appropriate laser energy ELaserThis allows an experimental determination of Eiiexpvalues 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 σ−πhybridization, thus lowering the electronic band energies, and (ii) the simple formulation of the tight binding model(γ0=2.89eV)to determine Eiistarts to deviate from Eiiexpfor tubes with dt<1.1nm but the deviation(formula presented)remains smaller than 20 meV for dt ∼0.83 nm A comparison between Eiiexpdata obtained from Raman and photoluminescence is made, and a comparison is also made between Eiiexpdata for SWNTs and double-wall carbon nanotubes.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Mar 26 2004|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics