We have performed microscopic calculations of the Rayleigh scattering cross section for arbitrary metallic single-walled carbon nanotubes. The focus of our investigations lies on excitonic effects and their influence on the characteristic features in a Rayleigh scattering spectrum. Our approach is based on density-matrix theory including tight-binding energies, the carrier-light coupling as well as the carrier-carrier interaction. Due to the refractive-index contribution to the scattering cross section, we observe characteristic features in Rayleigh spectra, such as a strong deviation from the Lorentz peak shape and the larger oscillator strength of the lower-lying transition $M_{ii}^{-}$ in the double-peaked structure, independently of the chiral angle and the diameter of the investigated nanotubes. We observe excitonic binding energies in the range of 60–80 meV for metallic nanotubes with diameters of 1.5–2.5 nm. The overlap of the excitonic transition with the close-by continuum has a significant influence on the peak shape and a minor influence on the peak intensity ratios. The presented results are in good agreement with recent experimental data.

• Received 27 January 2010

DOI:https://doi.org/10.1103/PhysRevB.82.115439