Quantum anomalous layer Hall effect in the topological magnet MnBi 2 Te 4

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) ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ [A. Gao et al., Nature (London) 595, 521 (2021)]. In this paper, we report that the quantization of LHE, which we call the quantum anomalous layer Hall effect (QALHE), can be realized in ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$. The QALHE originates from kicking a layer-locked Berry curvature monopole out of the Fermi sea by a vertical electric field. Remarkably, we demonstrate that 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 Berry curvature monopoles and quantized-layered transport in topological magnets.