Variational approach to excitons in carbon nanotubes

Excitons in quasi-one-dimensional semiconductors may lower the optical transition energies by a substantial amount. To quantify the effect in carbon nanotubes, we apply a simple variational approach. In excitonic units, a power law with exponent similar to-0.6 is obtained for the binding energy dependence on nanotube radius. When converted to ordinary units, the ratio of binding energy to tight-binding band gap yields a roughly constant value of nearly 40%. This substantial ratio implies that exciton effects are of prime importance for the optical properties of carbon nanotubes.