Classical Hall transition and magnetoresistance in strongly inhomogeneous planar systems

The magneto-transport properties of planar and layered strongly inhomogeneous two-phase systems are investigated, using the explicit expressions for the effective conductivities and resistivities obtained by the exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the effective resistivity of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. The corresponding plots of the x-dependence of the Hall constant RH(x,H) and the magnetoresistance R(x,H) are constructed for various values of magnetic field at some values of inhomogeneity parameters. These plots for strongly inhomogeneous systems at high magnetic fields show a sharp transition between partial Hall resistivities (or Hall conductivities) with different dependencies of RH on the phase concentrations. It is shown that there is a strong correlation between large linear magnetoresistance effect and this sharp Hall transition. Both these effects are a consequence of the exact duality symmetry. A possible physical explanation of these effects and their correlation is proposed.