Selective high harmonics generated from a carbon nanotube

Selective high-order harmonic radiation can be generated when circularly polarized driving fields interact with single-walled carbon nanotubes. We obtain a gauge-covariant Hamiltonian for electrons confined to a nanotube surface in the presence of a circularly polarized electromagnetic field. Regularized delta-functions are used to approximate the π-bonds in the nanotube unit cells and the electron dynamics, in the presence of the field, is analyzed. The high harmonic radiation occurs for incident field intensities high enough to induce significant nonlinearities and chaos in the electron dynamics. Both (5,5) and (10,10) armchair nanotubes are considered and the electron quantum dynamics is modeled using Floquet-Bloch theory. The behavior of the quasienergy spectrum, Floquet states, and the electron current density are described for varying intensities of the incident field. We show that, for incident radiation with frequency ω, the emitted radiation for a (p,p) armchair nanotube, will be (2p±1)ω, (4p±1)ω, etc.