Abstract
The Fano resonance spectra for the $G$ band in metallic carbon nanotubes are calculated as a function of laser excitation energy, in which the origin of the resonance is given by an interference between the continuous electronic Raman spectra and the discrete phonon spectra. We found that the second-order scattering process of the $\mathbf{q}\ensuremath{\ne}0$ electron-electron interaction is more relevant to the continuous spectra rather than the $\mathbf{q}=0$ first-order process because the $\mathbf{q}=0$ direct Coulomb interaction vanishes due to the symmetry of the two sublattices of a carbon nanotube.
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