Dependence of exciton transition energy of single-walled carbon nanotubes on surrounding dielectric materials

We theoretically investigate the environmental effect for optical transition energies of single-walled carbon nanotubes (SWNTs), by calculating the exciton transition energies of SWNTs. The static dielectric constants used in the exciton calculation can be expressed as a function of the dielectric constants of the surrounding material and that of the SWNT, in which the static and dynamic dielectric constants of the SWNT represent the screening effect of core electrons and the valence π electrons, respectively. The calculated results reproduce the environmental effect of the experimental transition energies for various surrounding materials and for various diameters of SWNTs.