Excitons and linear optical spectra of E33 and E44 in single wall carbon nanotubes under axial magnetic field

The E33 and E44 optical spectra of semiconducting single-walled carbon nanotubes under axial magnetic field (BB) are studied using the tight-binding model, which also takes into account the exciton effect. It is found that the E33 and E44 splitting, induced by the axial magnetic field, is line increased with magnetic field, which can be described by the splitting rate. Also by investigation of the dependence of splitting rate, we found that it shows a clear (2n+m2n+m) family behavior besides the diameter dependence, which can be used as a supplemental tool to identify the tubes used in the experiment, and is expected to be detected by the future experiment.