Chirality dependence of the dielectric constant for the excitonic transition energy of single-wall carbon nanotubes

Attention has been devoted recently to understand the physics behind the dielectric screening of the carbon nanotube optical transitions (E_ii), including how a changing environment changes E_ii. It was shown that the environmental screening could be modeled by an effective diameter dependent dielectric constant κ, which takes into account contributions from the single-wall carbon nanotube (SWNT) itself and from the environment surrounding the tube. Here we consider the chiral angle (θ) dependence of κ which improves the previous fitting by only the diameter dependence and we can now see the difference between E^M₁₁and E^S₂₂ by the present treatment. In this work we used the "alcohol-assisted" and the "super-growth" SWNT samples to address this point.