<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math>-band resonant Raman study of 62 isolated single-wall carbon nanotubes

We report G-band resonance Raman spectra of single-wall carbon nanotubes (SWNTs) at the single-nanotube level. By measuring 62 different isolated SWNTs resonant with the incident laser, and having diameters ${d}_{t}$ ranging between 0.95 nm and 2.62 nm, we have conclusively determined the dependence of the two most intense G-band features on the nanotube structure. The higher-frequency peak is not diameter dependent $({\ensuremath{\omega}}_{G}^{+}=1591 {\mathrm{cm}}^{\ensuremath{-}1}),$ while the lower-frequency peak is given by ${\ensuremath{\omega}}_{G}^{\ensuremath{-}}={\ensuremath{\omega}}_{G}^{+}\ensuremath{-}{C/d}_{t}^{2},$ with C being different for metallic and semiconducting SWNTs ${(C}_{M}>{C}_{S}).$ The peak frequencies do not depend on nanotube chiral angle. The intensity ratio between the two most intense features is in the range $0.1<{I}_{{\ensuremath{\omega}}_{G}^{\ensuremath{-}}}{/I}_{{\ensuremath{\omega}}_{G}^{+}}<0.3$ for most of the isolated SWNTs $(\ensuremath{\sim}90%).$ Unusually high or low ${I}_{{\ensuremath{\omega}}_{G}^{\ensuremath{-}}}{/I}_{{\ensuremath{\omega}}_{G}^{+}}$ ratios are observed for a few spectra coming from SWNTs under special resonance conditions, i.e., SWNTs for which the incident photons are in resonance with the ${E}_{44}^{S}$ interband transition and scattered photons are in resonance with ${E}_{33}^{S}.$ Since the ${E}_{\mathrm{ii}}$ values depend sensitively on both nanotube diameter and chirality, the $(n,m)$ SWNTs that should exhibit such a special G-band spectra can be predicted by resonance Raman theory. The agreement between theoretical predictions and experimental observations about these special G-band phenomena gives additional support for the $(n,m)$ assignment from resonance Raman spectroscopy.