We demonstrated theoretically that the renormalization of the electron energy
spectrum near the Dirac point of graphene by a strong high-frequency
electromagnetic field (dressing field) drastically depends on polarization of
the field. Namely, linear polarization results in an anisotropic gapless energy
spectrum, whereas circular polarization leads to an isotropic gapped one. As a
consequence, the stationary (dc) electronic transport in graphene strongly
depends on parameters of the dressing field: A circularly polarized field
monotonically decreases the isotropic conductivity of graphene, whereas a
linearly polarized one results in both giant anisotropy of conductivity (which
can reach thousands of percents) and the oscillating behavior of the
conductivity as a function of the field intensity. Since the predicted
phenomena can be observed in a graphene layer irradiated by a monochromatic
electromagnetic wave, the elaborated theory opens a substantially new way to
control electronic properties of graphene with light.Comment: Published versio