Electron-electron interaction effects on the optical excitations of semiconducting single-walled carbon nanotubes

Correlated-electron calculations of optically excited states in ten semiconducting single-walled carbon nanotubes with a wide range of diameters were discussed. It was shown that the optical excitation occurs to excitons whose binding energies decrease with increasing nanotube diameter and are smaller than the binding energy of an isolated strand of poly-(paraphenylene vinylene). It was found that the ratio of the second optical exciton polarized along the nanotube axis to that of the lowest exciton is smaller than the value predicted within single-particle theory. The results show that the experimentally observed weak photoluminescence is an intrinsic feature of semiconducting nanotubes.