Effect of periodic potential on exciton states in semiconductor carbon nanotubes

We develop a theoretical background to treat exciton states in semiconductor single-walled carbon nanotubes (SWCNTs) in the presence of a periodic potential induced by a surface acoustic wave (SAW) propagating along SWCNT. The formalism accounts for the electronic band splitting into the Floquet sub-bands induced by the Bragg scattering on the SAW potential. Optical transitions between the Floquet states and correlated electron-hole pairs (excitons) are numerically examined. Formation of new van Hove singularities within the edges of Floquet sub-bands and associated transfer of the exciton oscillator strengths resulting in the photoluminescence quenching are predicted. The simulations demonstrate the exciton energy red Stark shift and reduction in the exciton binding energy. Comparison of our results with reported theoretical and experimental studies is provided.