Localization effects on magnetotransport of a disordered Weyl semimetal

We study magnetotransport in a disordered Weyl semimetal taking into account localization effects exactly. In the vicinity of a Weyl node, a single chiral Landau level coexists with a number of conventional non-chiral levels. Disorder scattering mixes these topologically different modes leading to peculiar localization effects. We derive the average conductance as well as the full distribution function of transmission probabilities along the field direction. Remarkably, we find that localization of the non-chiral modes is greatly enhanced in a strong magnetic field with the typical localization length scaling as $1/B$. Technically, we use the non-linear sigma-model formalism with a topological term describing the chiral states. The problem is solved exactly by mapping to an equivalent transfer matrix Hamiltonian.