Exact Results on the Anomalous Hall Effect in a Dirac Semimetal

We study in detail the Berry curvature in Dirac semimetals across different regimes of its magnetic field dependence in terms of a "k.p model'' which is valid close to the Dirac point. Using analytical methods, we extract from this linear model exact predictions about the anomalous Hall effect that follow from the topology of the band structure and calculate how these change with the inclusion of Landau levels. These features can be discerned in the temperature and magnetic field dependence of the anomalous Hall effect, which we compare with recent experimental data in ZrTe₅ and with band structure calculations.