Though it is commonly accepted that the majority of graphene physics phenomena is properly described by massless pseudo-Dirac fermion approach, few unsolved problems (minimal graphene conductivity and carrier charge asymmetry) probably need for a new way to attack the problems. Recently we used the self-consistent Dirac-Fock-Hartree approximation to develop model for graphene-like materials. It has been shown that this model gives an estimates very near to experimental results on charge carrier concentration dependence of cyclotron mass. In the present work the proposed model for graphene is further developed on accounting of exchange effects (up to linear in k). Simulations performed have explicitly demonstrated the possibility of charge carrier asymmetry as well as existence of limiting case of massless pseudo-Dirac fermion model.
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