Topological Origin of Intrinsic High Chern Numbers in Two-Dimensional M${}_2$X${}_2$ Materials

Despite sharing a common lattice structure, monolayer M${}_2$X${}_2$ compounds realize quantum anomalous Hall phases with distinct Chern numbers, a striking phenomenon that has not been fully exploared. Combining first-principles calculations with symmetry analysis and tight-binding models, we identify two generic band-inversion mechanisms governed by the orbital composition and symmetry representations of 3$d$ states near the Fermi level. When $d_{xz}\mathrm{/}{d}_{yz}$ orbtials dominate, a doubly degenerate $\mathrm{\Gamma }$-point inversion yields $C=1$; otherwise, inversions occur along $\mathrm{\Gamma }$-X and $\mathrm{\Gamma }$-Y at four $C_4$-related momenta, whose Berry-curvature contributions add to give $C=2$, distinct from scenarios relying on multiple bands inversions at a single $\mathbf{k}$ point. The same mechanism consistently explains related two-dimensional systems, including LiFeSe, KTiSb, MgFeP, and Janus M${}_2$X${}_2$ derivatives. The mechanism provide practical guidance for screening and engineering tunable high-Chern-number insulators.