Magnetoresistance of Two-Dimensional Fermions in a Random Magnetic Field

TL;DR

This paper develops a new semiclassical method to calculate the magnetoresistance of 2D spinless fermions in a correlated random magnetic field, revealing a quadratic negative magnetoresistance in the weak field limit.

Contribution

A novel approach to solving the Boltzmann equation beyond the relaxation time approximation for this system.

Findings

Quadratic negative magnetoresistance in weak magnetic fields

Failure of the perturbative Born approximation in the relevant regime

Method applicable to systems with long-range correlated disorder

Abstract

We perform a semiclassical calculation of the magnetoresistance of spinless two-dimensional fermions in a long-range correlated random magnetic field. In the regime relevant for the problem of the half filled Landau level the perturbative Born approximation fails and we develop a new method of solving the Boltzmann equation beyond the relaxation time approximation. In absence of interactions, electron density modulations, in-plane fields, and Fermi surface anisotropy we obtain a quadratic negative magnetoresistance in the weak field limit.