Raman spectra of unfilled and filled carbon nanotubes: theory

Physical Review B, 76(16): pp. 165433-1-9.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 electronphonon 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. The Raman spectra of semiconducting unfilled and filled nanotubes have similar behaviors 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