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We present theoretical investigations on linear optical spectra and the temporal non-equilibrium dynamics of single-walled carbon nanotubes. In particular we discuss the importance of the surrounding medium. Our approach is based on the density matrix theory, which in combination with tight-binding wave functions allows the calculation of linear and nonlinear optical properties of arbitrary nanotubes. Its strength lies in the straightforward way to describe non-equilibrium properties, such as Coulomb driven ultrafast intrasubband carrier relaxation. We find a strong influence of the surrounding dielectric medium on the position of the peaks, the excitonic binding energy, and the carrier relaxation time. Furthermore, simple scaling laws describing the dependence on the dielectric background constant e bg are shown.

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 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.

Ultrafast intraband carrier relaxation in carbon nanotubes can be described by Carbon Nanotube Bloch Equations (CNBE) treating the Coulomb interaction beyond the Hartree-Fock level to include carrier-carrier scattering. We obtain equations of motion for carrier densities and two-particle carrier correlations that are solved numerically. The complex non-Markovian relaxation dynamics of hot electrons is calculated for various carbon nanotubes of different diameter and chirality. All calculated nanotubes show an ultrafast relaxation to equilibrium within approximately 100 femtoseconds. The observed relaxation is only weakly dependent on chirality, but depends on the diameter of the nanotube. With increasing diameter of the CNT the relaxation is slowed down, because of the weaker Coulomb interaction in larger diameter CNT. Additionally, we find oscillations of the electron plasma that are due to memory effects in the electron equilibration.

A microscopic calculation of the Rayleigh scattering cross section and the absorption coefficient for arbitrary single-walled carbon nanotubes is presented. The approach is based on the density matrix formalism combined with the tight-binding band structure. Both Rayleigh and absorption spectra show a characteristic intensity ratio behavior, which can be explained by an interplay of the optical matrix element and the joint density of states.

We illustrate the potential of the density matrix theory for investigation of optical properties of arbitrary single-walled carbon nanotubes (CNTs). We have performed microscopic calculations of excitonic absorption spectra for CNTs of different chiral angles and diameters. The obtained results are in good agreement with experiments, in particular the excitonic binding energies match well both experiments and ab initio calculations. Furthermore, we show the strength of our approach by presenting calculations of the ultrafast Coulomb driven non-equilibrium dynamics in CNTs. We find excitation induced dephasing on the picosecond time scale depending on the excitation strength. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)