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

Abstract: 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 $d{xz}/d_{yz}$ orbtials dominate, a doubly degenerate $\Gamma$-point inversion yields $C=1$; otherwise, inversions occur along $\Gamma$-X and $\Gamma$-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.