Excitonic absorption spectra of metallic single-walled carbon nanotubes

We present microscopic calculations of the absorption spectra of metallic single-walled carbon nanotubes. We address the controversial question of the excitonic binding energies in metallic nanotubes as well as the excitonic character of higher transitions. In spite of the strong screening, we observe binding energies in the range of 100 meV for metallic nanotubes with diameters in the range of 1-2.2 nm. Characteristic features of the absorption spectra, such as peak splitting and an asymmetric peak shape, are observed. The splitting is due to the trigonal warping effect. The peak shoulder at high energies is a result of an overlap of the excitonic excitation with the free-particle Van Hove singularity. Furthermore, we find higher transitions to be also significantly influenced by excitons. Our approach is based on density matrix, which allows the investigation of the chirality and diameter dependence of the excitonic binding energy for the first four optical transitions for a variety of different metallic and semiconducting nanotubes.