High frequency conductivity in carbon nanotubes

We report on theoretical analysis of high frequency conductivity in carbon nanotubes. Using the kinetic equation with constant relaxation time, an analytical expression for the complex conductivity is obtained. The real part of the complex conductivity is initially negative at zero frequency and become more negative with increasing frequency, until it reaches a resonance minimum at ω ∼ ω_B for metallic zigzag CNs and ω < ω_B for armchair CNs. This resonance enhancement is indicative for terahertz gain without the formation of current instabilities induced by negative dc conductivity. We noted that due to the high density of states of conduction electrons in metallic zigzag carbon nanotubes and the specific dispersion law inherent in hexagonal crystalline structure result in a uniquely high frequency conductivity than the corresponding values for metallic armchair carbon nanotubes. We suggest that this phenomenon can be used to suppress current instabilities that are normally associated with a negative dc differential conductivity.