Exciton ionization, Franz-Keldysh, and stark effects in carbon nanotubes

We calculate the optical properties of carbon nanotubes in an external static electric field directed along the tube axis. We predict strong Franz-Keldysh oscillations in the first and second band-to-band absorption peaks, quadratic Stark effect of the first two excitons, and the field dependence of the bound exciton ionization rate for a wide range of tube chiralities. We find that the phonon-assisted mechanism dominates the dissociation rate in electro-optical devices due to the hot optical phonons. We predict a quadratic dependence of the Sommerfeld factor on the electric field and its increase up to 2000% at the critical field of the full exciton dissociation.