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