Origin of the 2450 cm^-1 Raman bands in HOPG, single-wall and double-wall carbon nanotubes

The second order Raman signals around the G′-band region of graphite and carbon nanotubes have been investigated at more than 15 excitation laser lines. Two distinct Raman bands have been observed around 2700 cm^-1; a prominent one is due to the so-called G′-band and the other is a weak band around 2450 cm^-1. Both two bands can be from the double resonance process involving two phonons around the K-point in the phonon dispersion of a two-dimensional graphite. The 2450 cm^-1-band has exhibited little power dependence, whereas the intensity of G′-band has shown large photon energy dependence as already reported. The 2450 cm ^-1-band and the G′-band correspond to non-dispersive q = 0 and fully-dispersive q = 2k, respectively. From the phonon dispersion and the corresponding phonon frequency, the 2450 cm^-1-band can be assigned as an overtone mode of LO phonon (i.e. 2LO). This is revealed by calculated Raman spectra of graphite with proper electron-phonon matrix elements. The present study is the first report on the origin and assignment of the 2450 cm ^-1-band, which is based on the double resonance Raman scattering.