Zero m phonons in metal chalcogenide nanotubes

Phonon dispersions of single-wall MoS2 and WS2 nanotubes are calculated within a full symmetry implemented valence force-field model. Tubular structure is found to be characterized by two Raman active modes: by the in-phase breathing modes (in full analogy to carbon nanotubes) with frequency approaching Brillouin scattering domain (as diameter approaches nm), and by the high-energy breathing mode with sulfur shells breathing in phase, but out of phase relative to the Mo/W atoms. Likewise, the longitudinal rigid-shell mode, where sulfur shells vibrate out of phase whilst Mo/W atoms barely move, is predicted to be a fingerprint of the cylindrical configuration in infrared spectra. It is also found that twisting rigid-layer modes characterize chirality of the tubes. Finally, the large diameter limit is discussed and related to the measured Raman and infrared spectra of the layered structures