  The Raman spectra of two G-bands and a radial breathing mode (RBM) of
unfilled and filled single-wall semiconducting and metallic carbon nanotubes
have been investigated theoretically, in the presence of electron-phonon and
phonon-phonon interactions. Excitation of low frequency optical plasmons in the
metallic nanotube is responsible for the peak known as the Breit-Wigner-Fano
(BWF) line shape in the G-band Raman spectra. In a filled nanotube there is an
additional peak due to excitation of the phonon of the filling atom or
molecule. Positions, shapes and relative strengths of these Raman peaks depend
on the phonon frequencies of the nanotube and that of the filling atoms, and
strengths and forms of the plasmon-phonon and phonon-phonon interactions. For
example, filling atoms with phonon frequency close to the RBM frequency of the
nanotube may broaden and lower the RBM Raman peak to such an extent that it may
become barely visible. Hybridization between the G-bands and the filling atom
phonon is also strong when these two frequencies are close to each other and it
has important effects on the G-band and the BWF line shapes. When the phonon
frequency of the filling atom is far from the RBM and G-band frequencies, it
gives rise to a separate peak with modest effects on the RBM and G-band
spectra. Raman spectra of semiconducting unfilled and filled nanotubes have
similar behavior as those of metallic nanotubes except that normally they have
Lorentzian line shapes and do not show a BWF line shape. However, if a
semiconducting nanotube is filled with donor atoms, it is predicted that the
BWF type line shape may be observed near the RBM, or the G-band or the filling
atom Raman peak.
