Excitons in Carbon Nanotubes Revisited: Dependence on Diameter, Aharonov–Bohm Flux, and Strain

Optical spectra are calculated in semiconducting carbon nanotubes in the presence of magnetic flux and strain within a k · p scheme. The exciton absorption energies show an extra logarithmic dependence on the diameter after being scaled by the inverse diameter, coming from that of the enhancement of the band gaps. The exciton binding energy remains almost independent of the extra dependence. The ratio of the absorption energies of the first and second bands is ∼1.8 for the wide range of the effective interaction parameter. By the Coulomb interaction, the Aharonov–Bohm splitting in small magnetic flux is enhanced (5–10%) and the shift due to strain is also enhanced (10–20%).