Strong-field magnetotransport of two-phase disordered media in two and three dimensions: Exact and approximate results

Abstract

The electrical response of two-dimensional composites consisting of two isotropic normally conducting phases is studied. The composites are subject to a perpendicular magnetic field. An exact result is derived for the case where the areal fractions of the constituents are equal. In this case, the induced magnetoresistance is found to be linear in the magnetic field for strong fields. At other areal fractions, a saturating magnetoresistance is predicted by an analytical study of an effective medium approximation. An exception is found when the Hall resistivity is uniform throughout the medium. In this case, there is no induced magnetoresistance. The latter property also holds in an isotropic multiphase or spatially varying continuous medium characterized by a position-independent Hall resistivity. An asymptotic analysis of an effective medium approximation is also applied to a three-dimensional two-phase medium. Under certain conditions, involving charge carriers of opposite signs, this approximation predicts a unique behavior, different from the one predicted otherwise. The transverse ohmic resistivity is then increased relative to its value in ordinary cases, while the Hall resistivity asymptotically vanishes for a strong magnetic field. Explicit scaling functions for describing the crossover between the two distinct asymptotic behaviors are found. Finally, an effective medium approximation is applied to a three-dimensional two-phase composite with a uniform Hall resistivity. No induced magnetoresistance is predicted to appear in such a composite in the strong-field limit.