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 $R_H(x,H)$ 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 $R_H$ 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.