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.

We show theoretically that the strong interaction of a two-dimensional electron gas (2DEG) with a dressing electromagnetic field drastically changes its transport properties. Particularly, the dressing field leads to the giant increase of conductivity (which can reach thousands of percents), results in nontrivial oscillating dependence of conductivity on the field intensity, and suppresses the weak localization of 2DEG. As a consequence, the developed theory opens an unexplored way to control transport properties of 2DEG by a strong high-frequency electromagnetic field. From experimental viewpoint, this theory is applicable directly to quantum wells exposed to a lasergenerated electromagnetic wave.

Solving the Schrödinger problem for electrons in graphene subjected to both a stationary magnetic field and a strong high-frequency electromagnetic wave (dressing field), we found that the dressing field drastically changes the structure of Landau levels in graphene. As a consequence, the magnetoelectronic properties of graphene are very sensitive to the dressing field. Particularly, it is demonstrated theoretically that the dressing field strongly changes the optical spectra and the Shubnikov-de Haas oscillations. As a result, the developed theory opens a way for controlling magnetoelectronic properties of graphene with light.