Quasi-relativistic calculus of graphene monolayer minimal conductivity

We introduce a quasi-relativistic theory of quantum transport in graphene monolayer. It is based on the Dirac -- Hartry -- Fock self-consistent field approximation, assumption on lattice anti-ferromagnetic ordering and an approach [Falkovsky and Varlamov, Eur.~Phys.~J. {\bf B 56}, 281(2007)]. Minimal conductivity of graphene is shown to be $4.83$ (in units of $e^2/h$) when accounting for non-relativistic current only. Allowing for quasi-relativistic corrections to current due to process of pairs production and magneto-electric effects we obtain the results for the minimal conductivity which are in a very good agreement with experimental data for different supports.