Magnetoconductivity of Dirac semimetals and chiral magnetic effect from Keldysh technique

TL;DR

This work uses the Keldysh non-equilibrium formalism to establish a microscopic link between magnetoconductivity and the chiral magnetic effect in Dirac/Weyl semimetals under strong magnetic fields. By projecting to the lowest Landau level and including phonon- and impurity-induced dissipation, it derives a CME-like relation between axial charge density and current, with a computed chirality-relaxation time τ_5. The axial density ρ_5 and the conductivity σ follow the CME structure in the strong-field limit, with ε_B decomposed into phonon and impurity contributions and explicit expressions for χ and λ enabling quantitative comparisons to ZrTe_5 and related materials. The work also clarifies the role of ultraviolet regularization and lattice effects in chiral transport, providing a concrete microscopic mechanism for chiral relaxation in solid-state Dirac/Weyl systems.

Abstract

Negative magnetoresistance in Dirac semimetals is typically considered as a manifestation of chiral magnetic effect (CME). The relation between these two phenomena has the status of a hypothesis and is based on sequence of assumptions. We rely on the Keldysh technique of non-equilibrium theory. It allows us to investigate the accumulation of axial charge -- the process that involves both chiral anomaly and relaxation followed by the energy dissipation. We consider the case of strong magnetic field and calculate directly both axial charge density and electric conductivity taking into account both scattering on impurities and interaction with phonons. We obtain the same dependence of axial charge density on electric and magnetic fields, and the same dependence of electric current on axial charge density as the standard heuristic CME calculation. This confirms (in the limit of strong magnetic fields) the hypothesis that the origin of magnetoconductivity in Dirac semimetals is the CME.