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 kappa, which comprises the screening from the tube and from the environment. Different kappa dependencies are obtained for (E11(S), E22(S), E11(M)) relative to (E33(S), E44(S)). A changing environment changes the kappa diameter dependence for (E11(S), E22(S), E11(M)), but for (E33(S), E44(S)) the environmental effects are minimal. The resulting calculated exciton energies reproduce experimental E_{ii} values within +/-70 meV for a diameter range (0.7<d(t)<3.8 nm) and 1.2<Eii<2.7 eV, thus providing a theoretical justification for Eii, environmental effects and important insights on the dielectric screening in one-dimensional structures.