Dirac quantum kinetic equation: minimal conductivity revisited

Abstract

The kinetic equation used for the description of Dirac systems does not fully take into account two features that play an important role in the vicinity of the Dirac point: (i) the spin degree of freedom, in particular if the spin-flip energy $2 vp$ is not large anymore; and (ii) the failure of the semiclassical approximation due to the large Fermi wavelength. In our work, we propose a novel quantum kinetic equation, which does not have these two drawbacks. Exploiting it in the presence of short range disorder, we demonstrate how it predicts the correct minimal conductivity in 2D Dirac system, a result that has so far been obtained only by other methods like the Kubo formula. The nature of the presented kinetic equation opens up the possibility for the kinetic description of deeply quantum and even strongly correlated Dirac systems.