Field-controlled transport of Dirac particles with elliptical dispersion

We investigate tunneling and transport properties of Dirac electrons dressed by a linearly-polarized, off-resonance, and high-frequency dressing field through graphene and dice lattice sheets. We employ Floquet-Magnus perturbation theory to obtain the quasiparticle energy dispersion relation and closed form analytic expressions for dressed electron wave functions. We illustrate how features of the anomalous Klein paradox, i.e., a complete, asymmetrical electron transmission, which is independent on the barrier height or width, is modified by the anisotropic energy dispersion caused by the applied dressing field. We investigate the current strength and its dependence on the asymmetry introduced by Klein tunneling. The relationship of transmission current peaks to Klein tunneling maxima is examined. We predict a decrease in transmission current when the Klein transmission peak is located at a larger angle. We expect larger transmission current in the dice lattice than in graphene due to a much broader Klein tunneling peak in the former system. Predicted transport properties are expected to be useful in the design of novel electronic and optical graphene-based devices and electronic lenses in ballistic-electron optics.