P. S. Alekseev, A. P. Dmitriev, I. V. Gornyi, V. Yu. Kachorovskii
We study theoretically magnetoresistance of graphene with the short-range disorder. The key parameter determining magnetotransport properties - the product of the cyclotron frequency and transport scattering time, depends in graphene not only on magnetic field $H$ but also on electron energy $\varepsilon:$ $\omega_c\tau_q \propto H/\varepsilon^2 .$ As a result,"quantum" ($\omega_c\tau_q \gg 1 $) and "classical" ($\omega_c\tau_q \ll 1 $) regimes may coexist in the same sample at fixed $H,$ giving rise to a strong magnetoresistance. We calculate the conductivity tensor within the self-consistent Born approximation focusing on the case of relatively high temperature, when Shubnikov de Haas oscillations are suppressed by thermal averaging. We demonstrate that both at very low and at very high magnetic field the longitudinal resistivity scales as a square root of $H$: $[\varrho_{xx}(H) -\varrho_{xx}(0)]/\varrho_{xx}(0)\approx C \sqrt{H},$ where $C$ is temperature-dependent factor, different in the low- and strong-field limits. Furthermore, we predict a non monotonic dependence of the Hall coefficient both on magnetic field and on the electron concentration. Finally, we discuss the case of the charged impurity potential and also find a square-root low-field dependence of magnetoresistance near the Dirac point.
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http://arxiv.org/abs/1210.6081
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