Strong magnetoresistance of disordered graphene

We study theoretically magnetoresistance (MR) of graphene with different types of disorder. For short-range disorder, the key parameter determining magnetotransport properties---a product of the cyclotron frequency and scattering time---depends in graphene not only on magnetic field $H$ but also on the electron energy $\varepsilon$. As a result, a strong, square-root in $H$, MR arises already within the Drude-Boltzmann approach. The MR is particularly pronounced near the Dirac point. Furthermore, for the same reason, "quantum" (separated Landau levels) and "classical" (overlapping Landau levels) regimes may coexist in the same sample at fixed $H.$ We calculate the conductivity tensor within the self-consistent Born approximation for the case of relatively high temperature, when Shubnikov-de Haas oscillations are suppressed by thermal averaging. We predict a square-root MR both at very low and at very high $H:$ $[\varrho_{xx}(H)-\varrho_{xx}(0)]/\varrho_{xx}(0)\approx C \sqrt{H},$ where $C$ is a temperature-dependent factor, different in the low- and strong-field limits and containing both "quantum" and "classical" contributions. We also find a nonmonotonic dependence of the Hall coefficient both on magnetic field and on the electron concentration. In the case of screened charged impurities, we predict a strong temperature-independent MR near the Dirac point. Further, we discuss the competition between disorder- and collision-dominated mechanisms of the MR. In particular, we find that the square-root MR is always established for graphene with charged impurities in a generic gated setup at low temperature.