Optical conductivity of one-dimensional narrow-gap semiconductors

The optical conductivities of two one-dimensional narrow-gap semiconductors, anticrossing quantum Hall edge states and carbon nanotubes, are studied using bosonization method. A lowest order renormalization group analysis indicates that the bare band gap can be treated perturbatively at high frequency/temperature. At very low energy scale the optical conductivity is dominated by the excitonic contribution, while at temperature higher than a crossover temperature the excitonic features axe eliminated by thermal fluctuations. In case of carbon nanotubes the crossover temperature scale is estimated to be 300 K.