Number of Raman- and infrared-active vibrations in single-walled carbon nanotubes

By analyzing the point groups of the (nonsymmorphic) rod-groups of carbon nanotubes we show, for the first time, to the best of our knowledge, that all achiral carbon nanotubes possess only 8 Raman-active and 3 infrared-active phonon modes. This is in contrast to previously predicted 15--16 and 7-8 active modes, respectively. On the same ground we show that all chiral carbon nanotubes have 14 (instead of 15) Raman-active and 6 (instead of 9) infrared-active phonon modes.