On the origin of Abrikosov's quantum linear magnetoresistance

TL;DR

This paper derives Abrikosov's quantum linear magnetoresistance formula for Weyl semimetals using a new formalism, clarifying the conditions for its applicability and extending the theory to two-dimensional systems like graphene.

Contribution

The authors provide an exact derivation of Abrikosov's quantum linear magnetoresistance using diffusion of cyclotron orbits, clarifying the theory's assumptions and extending it to 2D systems.

Findings

Linear magnetoresistance occurs in the extreme quantum limit with Weyl fermions.

Both Weyl spectrum and smooth disorder are essential for the effect.

The derivation is extended to two-dimensional graphene-based systems.

Abstract

Compensated semimetals with Weyl spectra are predicted to exhibit unsaturated linear growth of their resistivity in quantizing magnetic fields. This so-called quantum linear magnetoresistance was introduced by Abrikosov, but approximations used in the theory remained poorly specified, often causing a confusion about experimental situations in which the analysis is applicable. Here we derive Abrikosov's exact result using an alternative formalism based on diffusion of cyclotron orbits in a random potential. We show that both Weyl spectrum and a disorder smooth on the scale of the magnetic length are essential conditions for the validity of the theory, and the linear magnetoresistance appears in the extreme quantum limit where only the zeroth Landau level is half filled. It is the interplay between the relativistic-like nature of Weyl fermions and the classical dynamics of their cyclotron centers, which leads to the linear magnetoresistance. We also derive an analogous result in two dimensions, which has been missing in the literature and is relevant for numerous graphene-based systems.