We present a microscopic calculation of the Rayleigh (elastic light) scattering spectra for single-walled carbon nanotubes. Combining density-matrix formalism and the tight-binding model, we obtain results for nanotubes of arbitrary chiral index. In agreement with experiment, the calculated Rayleigh spectra of metallic nanotubes show a double-peaked structure resulting from the trigonal warping effect, with the low-energy feature exhibiting greater intensity. We explain the intensity ratios by the wave-vector dependence of the optical matrix elements. Also in accord with experiment, the Rayleigh line shape of each peak is asymmetric, with an enhanced cross section for lower photon energies. This behavior arises from contributions of the nonresonant optical susceptibility to the Rayleigh scattering process.

• Received 10 June 2007

DOI:https://doi.org/10.1103/PhysRevB.77.045432