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The Haldane model on a honeycomb lattice is a paradigmatic example of asystem featuring quantized Hall conductivity in the absence of an externalmagnetic field, that is, a quantum anomalous Hall effect. Recent theoreticalwork predicted that the anomalous Hall conductivity of massive Dirac fermionscan display Shubnikov-de Haas (SdH) oscillations, which could be observed intopological insulators and honeycomb layers with strong spin--orbit coupling.Here, we investigate the electronic transport properties of Chern insulatorssubject to high magnetic fields by means of accurate spectral expansions oflattice Green's functions. We find that the anomalous component of the Hallconductivity displays visible SdH oscillations at low temperature.\textcolor{black}{The effect is shown to result from the modulation of thenext-nearest neighbour flux accumulation due to the Haldane term,} whichremoves the electron--hole symmetry from the Landau spectrum. To support ournumerical findings, we derive a long-wavelength description beyond the linear('Dirac cone') approximation. Finally, we discuss the dependence of the energyspectra shift for reversed magnetic fields with the topological gap and thelattice bandwidth.

Shubnikov-de Haas oscillations in the anomalous Hall conductivity of Chern insulators