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

We have studied intersubband decay of E 22 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 E 22 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 E 22 line widths are dominated by phonon assisted coupling to higher momentum states of the E 11 and E 12 exciton bands. The calculations also suggest that the branching ratio for decay into exciton bands vs free carrier bands, respectively is about 10:1.