Diameter Dependence of the Dielectric Constant for the Excitonic Transition Energy of Single-Wall Carbon Nanotubes

The measured optical transition energies E(ii) of single-wall carbon nanotubes are compared with bright exciton energy calculations. The E(ii) 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 (E(11)(S), E(22)(S), E(11)(M)) relative to (E(33)(S), E(44)(S)). A changing environment changes the kappa diameter dependence for (E(11)(S), E(22)(S), E(11)(M)), but for (E(33)(S), E(44)(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 < E(ii)< 2.7 eV, thus providing a theoretical justification for E(ii), environmental effects and important insights on the dielectric screening in one-dimensional structures.