Study of third-harmonic generation in zigzag carbon nanotubes using the Green function approach

We study the frequency behavior of third-order nonlinear optical harmonic of metallic and semiconductor zigzag carbon nanotubes. The tight binding model Hamiltonian is considered for electrons on the rolled honeycomb lattice. Based on the relation between nonlinear optical susceptibility and four current correlation function, the third harmonic can be obtained using Green's function. The effect of the radius of the nanotube on the susceptibility has been investigated. Furthermore, the role of temperature on the behavior of third-order harmonic is studied. The contribution of interband transitions due to the quantum aspects has been brought within the nonlinear response theory as a generalization of the Kubo formalism.