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Magnetoconductivity of Dirac semimetals and chiral magnetic effect from Keldysh technique

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.