Exciton dynamics in carbon nanotubes: from the Luttinger liquid to harmonic oscillators

We show that the absorption spectrum in semiconducting nanotubes can be determined using the bosonization technique combined with mean-field theory and a harmonic approximation. In this framework, a multiple band semiconducting nanotube reduces to a system of weakly coupled harmonic oscillators. We also find that gaps of any size destroy the Luttinger liquid phase in single-walled carbon nanotubes and give rise to electron density fluctuations that resemble excitons built from quasiparticles. Interband processes, such as multiple exciton generation, become progressively weaker as the length to diameter ratio grows larger.