Localization Effects on Magnetotransport of a Disordered Weyl Semimetal

We study longitudinal magnetotransport in a disordered Weyl semimetal taking into account localization effects in the vicinity of a Weyl node exactly. In a magnetic field, a single chiral Landau level coexists with a number of conventional nonchiral levels. Disorder scattering mixes these topologically different modes leading to very strong 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 nonchiral modes is greatly enhanced in a strong magnetic field with the typical localization length scaling as 1/B. Technically, we use the nonlinear sigma-model formalism with a topological term describing the chiral states. The problem is solved exactly by mapping to an equivalent transfer matrix Hamiltonian.