Coulomb effects on the fundamental optical transition in semiconducting single-walled carbon nanotubes: Divergent behavior in the small-diameter limit

We have experimentally investigated the diameter dependence of Coulomb effects on the optical transition in semiconducting single-walled carbon nanotubes. The absorption band due to the lowest band-to-band transition shifts to the higher-energy side compared to the transition energy calculated by a tight-binding model. The blueshift originating from the Coulomb effect increases with decreasing tube diameter d as $d^{-1.3}.$ We have found that this dependence is attributed to both the increase of the band gap and the enhancement of the exciton binding energy with a decrease of the diameter.