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

TL;DR

This paper presents an exact model for the high-field magnetoresistance in a macroscopically disordered 2D conductor, showing linear behavior at equal component fractions and saturation otherwise, with implications for disordered semiconductors.

Contribution

It introduces a duality-based exact solution for magnetoresistance in disordered conductors, highlighting conditions for linear versus saturating behavior.

Findings

At equal component fractions, magnetoresistance varies linearly with magnetic field.

For other compositions, magnetoresistance saturates at high fields.

The model connects to experimental observations in disordered chalconide semiconductors.

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.