Exciton energy Kataura plot and excitonic effect of single wall carbon nanotubes

We calculate exciton energy of single wall carbon nanotubes (SWNTs). The exciton energy depends on the surrounding materials of the SWNT [1]. This environmental effect is expressed by the dielectric constant [2]. In previous paper we used the static dielectric constant in order to reproduce the resonance Raman experiment for bundle samples [3,4]. However, since the dielectric constant depends on the nanotube diameter [5] and the surrounding materials, we need to consider a correction to the environmental effect for other samples. In this paper we discuss the environmental effect of SWNTs. The exciton energy of SWNTs is calculated by solving the Bethe-Salpeter equation in which the one particle energies are given by the extended tight-binding scheme [3]. We also compare our calculation with the resonance Raman experiments in the different environment. From our calculation we show the exciton energy Kataura plot for different samples.