Influence of strong screening effect on the perpendicular polarized linear excitonic absorption spectra of semiconducting carbon nanotubes

For incident light polarized perpendicular to the tube axis the multi-band semiconductor Bloch equations (MB-SBEs) that involve various screened interband Coulomb interactions (ICIs) are derived. The calculated E 12 peak is very close to the longitudinal excitonic peak E 22. Compared with the previous theoretical peak positions, the blue-shift of the peak in our results is about 0.5 eV. Then, subsequent detailed analyses show that the screening effect on the diagonal ICIs (D-ICIs) plays a key role in this big blue-shift. The valley-degenerate transverse pair excitations holding the same selection rule further enhance the screening effect on D-ICIs. Specially at q = 0 the dielectric function acting on the D-ICIs enhances two times. In our calculation the strong screening effect contributes 90% of the big blue-shift, while the non-diagonal ICIs (ND-ICIs) contribute to 10% of the blue-shift.