  Recently, a type of Hall effect due to an unusual layer-locked Berry
curvature called the layer Hall effect (LHE) has been reported in the
even-layered two-dimensional antiferromagnetic (AFM) MnBi2Te4 [A. Gao et.al,
Nature 595, 521 (2021)]. In this work, we report that the quantization of LHE,
which we call the quantum anomalous layer Hall effect (QALHE), can be realized
in MnBi2Te4. The QALHE originates from kicking a layer-locked Berry-curvature
monopole out of the Fermi sea by a vertielectric cal field. Remarkably, we
demonstrate that the electric-field reversal can switch the sign of the
quantized Hall conductance of QALHE in the even-layered AFM phase. The QALHE
can also be realized in the ferromagnetic phase. These results provide a
promising way toward the electric engineering of the Berry curvature monopoles
and quantized-layered transport in topological magnets.
