Relativistic correction to the magnetoresistance of the Dirac electron system

TL;DR

This paper derives a new relativistic correction to the magnetoresistance formula for Dirac electrons, providing a more accurate and field-dependent model that aligns with experimental observations and extends conventional Boltzmann theory.

Contribution

The paper introduces a relativistic correction to the Boltzmann-based magnetoresistance formula for Dirac electrons, improving its accuracy and field dependence analysis.

Findings

The new formula includes a relativistic correction not present in conventional theories.

The formula aligns quantitatively with Kubo theory except for quantum oscillations.

It explains the linear field dependence of MR in semimetals.

Abstract

The magnetoresistance (MR) for relativistic electrons, i.e., the Dirac electrons in solids, is investigated on the basis of the Boltzmann's theory. The new formula of MR so obtaiend includes a relativistic correction, which has not appeared in the conventional Boltzmann's theories. Our formula is quantitatively consistent with that obtained by the Kubo theory except for the quantum oscillations. While a field dependence of MR is unclear in the formula by Kubo theory, a clear field dependence is obtained in our formula, which is useful for the analysis of experimental results. The effects of the relativistic correction on the MR for the one-band and two-band model are discussed. By taking into account the field dependence of carrier density in semimetals, the linear field dependence of MR is explained by our formula based on the Boltzmann's theory