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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 antiferromagnetic MnBi2Te4 (F-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 F-MBT are analyzed. Interlayer ferroelectric polarization in F-MBT efficiently violates the PT symmetry (the combination symmetry of central inversion (P) and time reverse (T) of the F-MBT by conferring magnetoelectric couplings, and stabilizes a specific antiferromagnetic order encompassing a ferromagnetic interface in the F-MBT. We predict that engineering an interlayer polarization in the top or bottom interface of F-MBT allows converting F-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 bulk-like stacking forms of MnBi2Te4.

Recently, near-ambient superconductivity was claimed in nitrogen-doped lutetium hydride (LuH$_{3-\delta}$N$_{\epsilon}$) . Unfortunately, all follow-up research still cannot find superconductivity signs in successfully synthesized lutetium dihydride (LuH$_2$) and N-doped LuH$_{2\pm x}$N$_y$. However, a similar intriguing observation was the pressure-induced color changes (from blue to pink and subsequent red). The physical understanding of its origin and the correlation between the color, crystal structure, and chemical composition of Lu-H-N is still lacking. In this work, we theoretically study the optical properties of LuH$_2$, LuH$_3$, and some potential N-doped compounds using the first-principles calculations by considering both interband and intraband contributions. Our results show that LuH$_2$ has an optical reflectivity peak around blue light up to 10 GPa. Under higher pressure, the reflectivity of red light gradually becomes dominant. This evolution is driven by changes in the direct band gap and the Fermi velocity of free electrons under pressure. In contrast, LuH$_3$ exhibits gray and no color change up to 50 GPa. Furthermore, we considered different types of N-doped LuH$_2$ and LuH$_3$. We find that N-doped LuH$_2$ with the substitution of a hydrogen atom at the tetrahedral position maintains the color change when the N-doping concentration is low. As the doping level increases, this trend becomes less obvious. While other N-doped structures do not show significant color change. Our results can clarify the origin of the experimental observed blue-to-red color change in lutetium hydride and also provide a further understanding of the potential N-doped lutetium dihydride.