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

Abstract

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 (E[subscript 11]S, E[subscript 22]S, E[subscript 11]M) relative to (E[subscript 33]S, E[subscript 44]S). A changing environment changes the κ diameter dependence for (E[subscript 11]S, E[subscript 22]S, E[subscript 11]M), but for (E[subscript 33]S, E[subscript 44]S) the environmental effects are minimal. The resulting calculated exciton energies reproduce experimental Eii values within ±70 meV for a diameter range (0.7<dt<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.