Derivation of the screened Bloch equations and application to carbon nanostructures

Optical properties of single-walled semiconducting and metallic carbon nanotubes are significantly influenced by excitonic effects. The excitonic binding energy strongly depends on Coulomb screening. Here, we show-using a non-perturbative single-time equation of motion method-how the momentum-dependent dielectric function (q) for carbon nanotubes can be consistently derived within a microscopic theory. We investigate the influence of the corresponding screening on the absorption spectra of semiconducting and metallic carbon nanotubes. We observe clearly smaller excitonic binding energies for metallic nanotubes arising from an efficient screening stemming from the crossing bands. The presented method can be applied in a straightforward way to calculate the Coulomb screening in other nanostructures, such as graphene and carbon nanoribbons.