Second-order harmonic and combination modes in graphite, single-wall carbon nanotube bundles, and isolated single-wall carbon nanotubes

We report a study of second-order combination and overtone modes in highly ordered pyrolytic graphite (HOPG), in single-wall carbon nanotube (SWNT) bundles and in isolated SWNTs. We found both dispersive and nondispersive Raman bands in the range $1650–2100{\mathrm{cm}}^{-1},$ and we show that the appearance and frequency versus laser energy $E_{\mathrm{laser}}$ behavior of these features are in agreement with predictions from double-resonance Raman theory. In the case of SWNTs, these second-order bands depend on the one-dimensional structure of SWNTs, and at the single nanotube level, the spectra vary from tube to tube, depending on tube diameter and chirality and on the energy of the van Hove singularity relative to $E_{\mathrm{laser}}.$