Raman spectra of double-walled carbon nanotubes

Using nonresonant bond-polarization theory, Raman spectra of periodic double-walled carbon nanotubes (DWCNTs) are calculated. Due to the lower symmetry of DWCNT, the number of Raman active modes is much larger compared to those of its layers. Complete frequency range of the tubes spectra has been analyzed for large number of tubes. We found that only modes whose frequencies are below 800 cm(-1) have noticeable up shifts compared to those of isolated layers. Special attention is given to radial breathing modes (RBMs) and G-band region since these modes are used for the identification of singe-walled carbon nanotubes. In case of breathing like modes (BLMs), frequency of the out of phase mode is found to be chirality dependent, while the in phase one remains only diameter dependent as in the case of individual layers.