Interlayer ferroelectric polarization modulated anomalous Hall effect in four-layer $\mathrm{MnB}{i}_{2}T{e}_4$ antiferromagnets

Van der Waals (vdW) assembly could efficiently modulate the symmetry of two-dimensional (2D) materials that ultimately governs their physical properties. Of particular interest is the ferroelectric polarization being introduced by proper vdW assembly that enables the realization of novel electronic, magnetic, and transport properties of 2D materials. Four-layer bulklike stacking antiferromagnetic $\mathrm{MnB}{i}_{2}T{e}_4$ ($\mathrm{FB}$-MBT) offers an excellent platform to explore ferroelectric polarization effects on magnetic order and topological transport properties of nanomaterials. Here, by applying symmetry analyses and density-functional-theory calculations, the ferroelectric interface effects on magnetic order, anomalous Hall effect (AHE) or even quantum AHE (QAHE) on the $\mathrm{FB}$-MBT are analyzed. Interlayer ferroelectric polarization in $\mathrm{FB}$-MBT efficiently violates the $\hat{P}\hat{T}$ symmetry [the combination of central inversion ($\hat{P}$) and time reverse ($\hat{T}$) symmetry] of the $\mathrm{FB}$-MBT by conferring magnetoelectric couplings, and stabilizes a specific antiferromagnetic order encompassing a ferromagnetic interface in the $\mathrm{FB}$-MBT. We predict that engineering an interlayer polarization in the top or bottom interface of $\mathrm{FB}$-MBT allows converting $\mathrm{FB}$-MBT from a trivial insulator to a Chern insulator. The switching of ferroelectric polarization at the middle interfaces results in a direction reversal of the quantum anomalous Hall current. Additionally, the interlayer polarization of the top and bottom interfaces can be aligned in the same direction, and the switching of polarization direction also reverses the direction of anomalous Hall currents. Overall, our work highlights the occurrence of quantum-transport phenomena in 2D vdW four-layer antiferromagnets through vdW assembly. These phenomena are absent in the bulk or thin-film in bulklike stacking forms of $\mathrm{MnB}{i}_{2}T{e}_4$.