Hall conductivity of a two-dimensional graphite system

Within a self-consistent Born approximation, the Hall conductivity of a two-dimensional graphite system in the presence of a magnetic field is studied by quantum transport theory. The Hall conductivity is calculated for short- and long-range scatterers. It is calculated analytically in the limit of strong magnetic fields and in the Boltzmann limit in weak magnetic fields. The numerical calculation shows that the Hall conductivity displays the quantum Hall effect when the Fermi energy is in low-lying Landau levels and the scattering is weak. When the Fermi energy becomes away from $\varepsilon =0,$ it tends to the Boltzmann result.