Electrodynamics of chiral carbon nanotubes in the helical parametrization scheme

Basic equations of electrodynamics of carbon nanotubes (CNTs) are formulated in the helical parametrization scheme, where the crystalline structure of non-zigzag (n₁, n₂) CNTs is described as a set of n₂ double helices, and the electron energy spectrum of the CNTs consists of n2 different helicoidal branches. The parametrization scheme is shown to be natural and more convenient for analyzing the electromagnetic response properties of chiral CNTs. Bloch equations for the density matrix have been obtained and adapted for the helical parametrization that allows studying the interaction between chiral CNTs and electromagnetic fields with arbitrary polarization and spatial structure. Linear transverse conductivity of chiral CNTs has been derived and utilized for the formulation of the effective boundary conditions for electromagnetic field on the surface of a chiral CNT. As an example, the spectra of high-order harmonics in chiral CNTs have been evaluated from the Bloch equations.