High energy E$_{11}$ excitons above the continuum threshold in semiconducting single-walled carbon nanotubes

Although the excitonic nature of the primary photoexcitation has been firmly established in semiconducting single-walled carbon nanotubes (S-SWCNTs), the magnitude of the exciton binding energy is still being debated. Recent photoluminescence excitation experiments have detected excitons above the threshold of the continuum band predicted from two-photon absorption measurements in the (10,6) S-SWCNT \footnote{J. Lefebvre and P. Finnie, Nano Lett. \textbf{8}, 1890 (2008).} One interpretation of this experiment is that the exciton binding energy is much larger than previous estimates \footnote{J. Deslippe et al., Nano Lett. \textbf{9}, 1330 (2009).} We have performed configuration interaction calculations for the (10,6) S-SWCNT within the molecular PPP model that quantitatively reproduces the earlier estimate for the exciton binding energy and also finds excitons deep inside the continuum. A similar observation has previously been made for the conjugated polymer PPV.