Magneto-conductivity and CME in Dirac semimetals from Keldysh technique in Landau levels basis

Negative magnetoresistance in Dirac semimetals is conventionally considered as a manifestation of chiral magnetic effect (CME), by means of a postulated Chiral Kinetic equation. In this paper we study magnetoconductivity in large Fermi energy Dirac semimetals, in one of which (ZrTe$_5$) the effect was observed for the first time. Starting with a Hamiltonian for a semi-realistic model of such a Dirac semimetal, we apply the Non-equilibrium Diagram Technique (NDT, or the Keldysh technique) to derive the kinetic equations, to investigate the electrons relaxation due to interaction with phonons and disorder, and, finally, to calculate the DC magnetoconductivity (the longitudinal to magnetic field component of conductivity) as a function of magnetic field strength and temperature. Finally, we compare the obtained temperature dependencies with available to us experimental data.