Excitonic Rayleigh scattering spectra of metallic single-walled carbon nanotubes

Abstract

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 ${M}_{ii}^{\ensuremath{-}}$ 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.