  Van der Waals (vdW) assembly allows controlling symmetry of two-dimensional
(2D) materials that determines their physical properties. Especially
interesting is the recently demonstrated breaking inversion symmetry by polar
layer stacking to realize novel electronic, magnetic, and transport properties
of 2D vdW materials switchable by induced electric polarization. Here, based on
symmetry analyses and density-functional calculations, we explore the emergence
of the anomalous Hall effect (AHE) in antiferromagnetic MnBi2Te4 films
assembled by polar layer stacking. We demonstrate that breaking PT symmetry in
an MnBi2Te4 bilayer makes this 2D material magnetoelectric and produces a
spontaneous AHE switchable by electric polarization. We find that reversable
polarization at one of the interfaces in a three-layer MnBi2Te4 film drives a
metal-insulator transition, as well as switching between an AHE and quantum AHE
(QAHE). Finally, we predict that engineering an interlayer polarization in a
three-layer MnBi2Te4 film allows converting MnBi2Te4 from a trivial insulator
to a Chern insulator. Overall, our work emphasizes the emergence of
quantum-transport phenomena in 2D vdW antiferromagnets by polar layer stacking,
which do not exist in this material in the bulk or bulk-like thin-film forms.
