Diameter dependence of the dielectric constant for the excitonic transition energy of single-wall carbon nanotubes

The measured optical transition energies Eii of single-wall carbon nanotubes are compared with bright exciton energy calculations. The Eii differences between experiment and theory are minimized by considering a diameter-dependent dielectric constant κ, which comprises the screening from the tube and from the environment. Different κ dependencies are obtained for (E11S, E22S, E11M) relative to (E33S, E44S). A changing environment changes the κ diameter dependence for (E11S, E22S, E11M), but for (E33S, E44S) the environmental effects are minimal. The resulting calculated exciton energies reproduce experimental Eii values within ±70meV for a diameter range (0.7<dt<3.8nm) and 1.2<Eii<2.7eV, thus providing a theoretical justification for Eii, environmental effects and important insights on the dielectric screening in one-dimensional structures.