Specifc boundary conditions and enhanced transmission in a dice lattice under linearly polarized dressing field*

We have investigated electron tunneling for a dice lattice in the presence of linearly polarized external dressing fied. Linearly polarized irradiation leads to a finite anisotropy of the Dirac energy dispersion relations of the investigated material, and a specific type of the wave functions for the dressed electron states. The direction of the light polarization can be generally different from the direction of incoming electrons. Such a finite misalignment angle together with the dispersion
anisotropy are related to the asymmetric Klein paradox. In order to do the tunneling problem we needed to derive an absolutely new type of boundary conditions which include the intensity of the applied light and it's direction of its polarization. The obtained boundary relations, which are not equivalent to such conditions in graphene and for non-irradiated dice lattice, are in the focus of this
work.