Rectification due to harmonic mixing of two coherent electromagnetic waves with commensurate frequencies in carbon nanotubes

We report on a theoretical investigation of carbon nanotubes subjected to a pure alternating electric field consisting of two phase-shifted harmonic fields of frequencies ω₁ = Ω and ω₂ = 2Ω (harmonic mixing) without any direct current bias. We employed a tight-binding approximation for the description of the energy bands of the carbon nanotubes and the Boltzmann transport equation with constant relaxation time approximation. The results are compared to that of a superlattice under similar conditions. The results indicate a direct current generation by the carbon nanotubes due to the harmonic mixing. The described effect is in essence, due to the nonlinearity associated with the non-parabolicity of the electron energy band, which is greater in the carbon nanotubes than the superlattices. The strong effect observed in the carbon nanotubes is attributed to the stark components and the specific dispersion law inherent in hexagonal crystalline structure of the carbon nanotubes.