  Dirac fermions are actively investigated, and the discovery of the quantized
anomalous Hall effect of massive Dirac fermions has spurred the promise of
low-energy electronics. Some materials hosting Dirac fermions are natural
platforms for interlayer coherence effects such as Coulomb drag and exciton
condensation. Here we determine the role played by the anomalous Hall effect in
Coulomb drag in massive Dirac fermion systems. We focus on topological
insulator films with out-of plane magnetizations in both the active and passive
layers. The transverse response of the active layer is dominated by a
topological term arising from the Berry curvature. We show that the topological
mechanism does not contribute to Coulomb drag, yet the longitudinal drag force
in the passive layer gives rise to a transverse drag current. This anomalous
Hall drag current is independent of the active-layer magnetization, a fact that
can be verified experimentally. It depends non-monotonically on the
passive-layer magnetization, exhibiting a peak that becomes more pronounced at
low densities. These findings should stimulate new experiments and quantitative
studies of anomalous Hall drag.
