Intersubband decay of 1-D exciton resonances in carbon nanotubes.

We have studied intersubband decay of E22 excitons in semiconducting carbon nanotubes experimentally and theoretically. Photoluminescence excitation line widths of semiconducting nanotubes with chiral indicess (n,m) can be mapped onto a connectivity grid with curves of constant (n - m) and (2n + m). Moreover, the global behavior of E22 line widths is best characterized by a strong increase with energy irrespective of their (n-m)mod(3) = +/-1 family affiliation. Solution of the Bethe-Salpeter equations shows that the E22 line widths are dominated by phonon assisted coupling to higher momentum states of the E11 and E12 exciton bands. The calculations also suggest that the branching ratio for decay into exciton bands vs free carrier bands, respectively is about 10:1.