Uniform Peak Optical Conductivity In Single-Walled Carbon Nanotubes

Recent Rayleigh scattering measurements show that all single-walled carbon nanotubes have a peak optical conductivity of approximately 8 e(2)/h, independent of radius, chiral angle, or whether the nanotube is semiconducting or metallic [D. Y. Joh et al., Nat. Nanotechnol. 6, 51 ( 2011)]. We show that this uniform peak conductivity is a consequence of the relativistic band structure and strength of the Coulomb interaction in carbon nanotubes. We also show that a simple exciton model accurately describes the general phenomenology and the numerical value of the peak optical conductivity. Our work illustrates the need for careful treatment of relaxation mechanisms in modeling the optoelectronic properties of carbon nanotubes.