Charge impurity as a localization center for singlet excitons in single-wall nanotubes

A simple model is developed for studying the interaction of bright excitons in semiconducting single-wall nanotubes with charged impurities. The model reveals redshift in the energy of excitonic states in the presence of impurity, thus indicating binding of free excitons in the impurity potential well. Several bound states were found in absorption spectrum below the onset of excitonic optical transitions in the bare nanotube. Dependence of the binding energy on the model parameters, such as impurity charge and position, was determined and analytical fits were derived for a number of tubes of different diameter. The nanotube family splitting is seen in the diameter dependence, gradually decreasing with the diameter. By calculating the partial absorption coefficient for a small segment of nanotube, the local nature of the wave function of the bound states was derived.