Scaling of excitons in carbon nanotubes

The excitonic properties of carbon nanotubes embedded in dielectric medium for the range of tube radii and dielectric constants were investigated. The simple scaling relationships showed strong relations between the binding energy, exciton size, and oscillator strength. The approximate calculations show that the effective mass m depends on the tube indices. The exciton size was found to affect directly the observable quantities such as the exciton oscillator strength and the radiative lifetime. The results show the exciton strength is proportional to the probability to find an electron and a hole at the same position.