AC conductivity of metallic carbon nanotubes (CNTs) exposed to a DC field

The AC conductivity of a carbon nanotube (CNT) is derived and it is shown that it can become negative when the CNT is exposed to a DC axial field in addition to the AC field. For this purpose, the Boltzmann transport equation (BTE) is solved within the relaxation time approximation (RTA) by separating the AC and DC contributions. The near-equilibrium approximation is used for the DC part of the carrier distribution. The AC carrier distribution and the AC conductivity are subsequently found via a semi-analytical procedure. Absolute negative AC conductivity is found at for a DC field above 10⁵ V/m, which is a promising result toward enabling CNT traveling-wave amplifiers.