Probing the electronic trigonal warping effect in individual single-wall carbon nanotubes using phonon spectra

We have studied the trigonal warping effect in metallic carbon nanotubes using resonance Raman scattering and examining the G ′-band profile for individual metallic single-wall carbon nanotubes. We show that the observed splitting in the G ′-band phonon spectra is directly correlated with the splitting in the singularities of the joint density of electronic states, i.e., detailed information about the 1D electronic structure is extracted from a phonon measurement. By correlating the phonon data with the calculated electronic structure for several (n,m) nanotubes, we were able to determine the G ′-band dispersion [(∂ωG′ /∂E laser )=108±6 cm −1/eV] by using a single laser energy.