Influence of Coulomb-induced band couplings on linear excitonic absorption spectra of semiconducting carbon nanotubes

Starting from the extended Su-Schrieffer-Heeger model, multiband semiconductor Bloch equations are formulated in momentum space and applied to the analysis of the linear optical response of semiconducting carbon nanotubes (SCNTs). This formalism includes the coupling of electron-hole pair excitations between different valence and conduction bands, originating from the electron-hole Coulomb attraction. The influence of these couplings, which are referred to as nondiagonal interband Coulomb interaction (NDI-CI), on the linear excitonic absorption spectra is investigated and discussed for light fields polarized parallel to the tube direction. The results show that the intervalley NDI-CI leads to a significant increase of the band gap and a decrease of the exciton binding energy that results in a blueshift of the lowest-frequency excitonic absorption peak. The strength of these effects depends on the symmetry of the SCNT. Furthermore, for zigzag SCNTs with higher symmetry other nonintervalley NDI-CI terms also affect the spectral positions of excitonic absorption peaks.