Anomalous Hall effect in the Dirac electron system with a split term

We study an anomalous Hall effect in the massive Dirac electron system with broken time reversal symmetry. Using the model Hamiltonian with the spin-orbit interaction and a split term which breaks time reversal symmetry, we calculate the energy band, the Berry curvature and the intrinsic Hall conductivity in an analytical way. We show that the nonzero Berry curvature appears and thus an intrinsic Hall conductivity occurs. This anomalous Hall effect can be observed in such systems as a ferromagnetic Dirac electron system or a ferromagnet-coated Dirac electron system.