The valley index is a promising degree of freedom for information processing in electronic devices. However, the researches on valley polarization are mainly focused on ferromagnetic order, which breaks the time reversal symmetry simultaneously. Here, a novel paradigm for achieving stacking order modulated anomalous valley Hall (AVH) effect is proposed in antiferromagnetic monolayers. The paradigm involves the introduction and reversal of nonuniform potentials by modulating the position of substrate, to break the combined symmetry of spatial inversion and time reversal (PT symmetry) and achieve stacking-dependent valley spin splitting. Based on first-principles calculations, we discover spontaneous valley polarization in antiferromagnetic Cr₂CH₂ MXene and stacking-dependent valley spin splitting in Cr₂CH₂/Sc₂CO₂ heterostructure. Furthermore, switching the ferroelectric polarization of monolayer Sc₂CO₂ results in a semiconductor-metal transition in Cr₂CH₂/Sc₂CO₂, accompanied by the disappearance of valley physics. Our findings provide an alternative way to develop controllable valleytronics devices based on antiferromagnetic monolayers.

The electrocatalytic nitrogen reduction reaction (NRR) is currently constrained by sluggish reaction kinetics and poor selectivity because of the difficulties in activating inert N≡N triple bonds and the existence of competing hydrogen evolution reaction (HER). Therefore, electrocatalysts with high activity, selectivity, and stability are highly desired. Herein, by means of first-principles calculations, we investigated the electrocatalytic NRR performance of a series of transition metal atoms (e.g., 3d, 4d, and 5d) embedded in defective hexagonal MBene nanosheets [h-Zr(Hf)₂B₂O₂] and identified that h-Zr(Hf)₂B₂O₂ could be an excellent platform for electrocatalytic NRR. On the basis of our proposed screening criteria, 16 candidates are efficiently selected out from 50 systems, among which, Zr₂B₂O₂-Cr stands out with high selectivity to NRR against HER and the ultralow limiting potential (−0.10 V). The value is much lower than that of the well-established stepped Ru(0001) surface (−0.43 V). The origin of the high activity toward NRR is attributed to the synergistic effect of the single atom (SA) and the M atoms in the substrate. More impressively, a composition descriptor is further proposed on the basis of the inherent characteristics of the catalysts [number of valence electrons of SA and electronegativity of the SA and Zr(Hf) atoms], which helps to better predict the catalytic performance. Our work not only contributes to the development of highly efficient NRR electrocatalysts but also extend the application of h-MBenes in electrocatalysis.