  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.
