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Raman scattering (RS) spectra and current-voltage characteristics at room temperature were measured in six series of small samples fabricated by means of electron-beam lithography on the surface of a large size (5x5 mm) industrial monolayer graphene film. Samples were irradiated by different doses of C${}^+$ ion beam up to $10^{15}$ cm${}^{-2}$. It was observed that at the utmost degree of disorder, the Raman spectra lines disappear which is accompanied by the exponential increase of resistance and change in the current-voltage characteristics.These effects are explained by suggestion that highly disordered graphene film ceases to be a continuous and splits into separate fragments. The relationship between structure (intensity of RS lines) and sample resistance is defined. It is shown that the maximal resistance of the continuous film is of order of reciprocal value of the minimal graphene conductivity $\pi h/4e^2\approx 20$ kOhm.Comment: 5 pages, 5 eps figures. As accepted for publication in PR

Gradual localization of charge carriers was studied in a series of micro-size samples of monolayer graphene fabricated on the common large scale film and irradiated by different doses of C + ions with energy 35 keV. Measurements of the temperature dependence of conductivity and magnetoresistance in fields up to 4 T showed that at low disorder, the samples are in the regime of weak localization and antilocalization. Further increase of disorder leads to strong localization regime, when conductivity is described by the variable-range-hopping (VRH) mechanism. A crossover from the Mott regime to the Efros-Shklovskii regime of VRH is observed with decreasing temperature. Theoretical analysis of conductivity in both regimes showed a remarkably good agreement with experimental data.

Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A "collective variable approach" technique, based on trial functions, is used for solution of the general nonlinear Schrödinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon-"beats" of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.