Lattice dynamics of single-walled carbon nanotubes

In this paper, the theory of lattice dynamics of single-walled carbon nanotubes is presented. The screw symmetry of the system is used to reduce the rank of the dynamical matrix to six, independent of the number of atoms in the unit cell. Calculations of the lattice dynamics are carried out within a valence force field model and of the Raman intensity—within a bond-polarizability model. It is found that the breathing mode frequency is inversely proportional to the radius of the tube that can be used for the characterization of the samples on the basis of Raman-scattering data. The results for the Raman intensity are compared to available Raman spectra.