Model for a Macroscopically Disordered Conductor with an Exactly Linear High-Field Magnetoresistance

Abstract

We calculate the effective resistivity of a macroscopically disordered two dimensional conductor consisting of two components in a perpendicular magnetic field. When two components have equal area fractions, we use a duality theorem to show that the magnetoresistance is non-saturating and at high fields varies exactly linearly with magnetic field. At other compositions, an effective medium calculation leads to a saturating magnetoresistance. We briefly discuss possible connections between these results and magnetoresistance measurements on heavily disordered chalconide semiconductors.