Origin of coherent G -band phonon spectra in single-wall carbon nanotubes

Coherent phonons in single-wall carbon nanotubes (SWNTs) are observed as oscillations of the differential absorption coefficient as a function of time by means of pump-probe spectroscopy. For the radial breathing mode (RBM) of a SWNT, the coherent phonon signal is understood to be a result of the modulated diameter-dependent energy gaps due to the coherent RBM phonon oscillations. However, this mechanism might not be the dominant contribution to other phonon modes in the SWNT. In particular, for the G-band phonons, which correspond to bond-stretching motions, we find that the modulation of the interatomic optical dipole (electron-photon) matrix element gives rise to a strong coherent G-band phonon intensity comparable to the coherent RBM phonon intensity. We also further discuss the dependence of coherent G-band and RBM phonon amplitudes on the laser excitation pulse width.