Theory of Two Dimensional Mean Field Electron Magnetohydrodynamics

The theory of mean field electrodynamics for diffusive processes in Electron Magnetohydrodynamic (EMHD) model is presented. In contrast to Magnetohydrodynamics (MHD) the evolution of magnetic field here is governed by a nonlinear equation in the magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whisterlization of the spectrum, the turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whisterlization is observed. Numerical studies also show the suppression of magnetic field diffusivity in accordance with the analytical estimates.Comment: 18 pages, 6 figure

Graphene magnetoresistance in a parallel magnetic field: Spin polarization effect

We develop a theory for graphene magnetotransport in the presence of carrier spin polarization as induced, for example, by the application of an in-plane magnetic field ($B$) parallel to the 2D graphene layer. We predict a negative magnetoresistance $\sigma \propto B^2$ for intrinsic graphene, but for extrinsic graphene we find a non-monotonic magnetoresistance which is positive at lower magnetic fields (below the full spin-polarization) and negative at very high fields (above the full spin-polarization). The conductivity of the minority spin band $(-)$ electrons does not vanish as the minority carrier density ($n_-$) goes to zero. The residual conductivity of $(-)$ electrons at $n_- = 0$ is unique to graphene. We discuss experimental implications of our theory.Comment: 5 pages, 3 figure