  We find that the optical properties of carbon nanotubes reflect remarkably
strong effects of exciton-phonon coupling. Tight-binding calculations show that
a significant fraction of the spectral weight of the absorption peak is
transferred to a distinct exciton+phonon sideband, which is peaked at around
200 meV above the main absorption peak. This sideband provides a distinctive
signature of the excitonic character of the optical transition. The
exciton-phonon coupling is reflected in a dynamical structural distortion,
which contributes a binding energy of up to 100 meV. The distortion is
surprisingly long-ranged, and is strongly dependent on chirality.
