Coulomb effects in single-walled carbon nanotubes

We present microscopic calculations of the excitonic absorption coefficient for single-wall carbon nanotubes. Our approach combines the density matrix formalism including the Coulomb and electron-light interaction with the tight-binding approximation. It allows the investigation of excitons in carbon nanotubes of arbitrary chiral index over a wide range of energy. We take all intra- and intersubband contributions into account and study the behavior of the Coulomb matrix elements for all relevant processes. The Coulomb interaction is found to decrease strongly with increasing momentum transfer perpendicular to the nanotube axis. Furthermore, we show that the band gap renormalization arising from the electron-electron interaction leads to a partial lifting of degeneracy in the spectra of zig-zag tubes. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim