Induced nonlinear cross sections of conductive electrons scattering on the charged impurities in doped graphene

Relativistic quantum theory of induced scattering of 2D Dirac particles by electrostatic field of impurity ion (in the Born approximation) in the doped graphene at the presence of an external electromagnetic radiation field (actually terahertz radiation, to exclude the valence electrons excitations at high Fermi energies) has been developed. It is shown that the strong coupling of massless quasiparticles in the quantum nanostructures to a strong electromagnetic radiation field leads to the strongly nonlinear response of graphene, which opens diverse ways for manipulating the electronic transport properties of conductive electrons by coherent radiation fields.