Bilateral hydrogenation induced high-Chern-number quantum anomalous Hall state in monolayer Cr$_2$Ge$_2$Te$_6$
The pursuit of high-temperature quantum anomalous Hall (QAH) insulators faces fundamental challenges, including narrow topological gaps and low Curie temperatures ($T_C$) in existing materials. Here, we propose a strategy using bilateral hydrogenation to engineer a robust QAH state in the topologically trivial ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$ via covalent orbital reconstruction. First-principles calculations reveal that by rewiring the orbital hybridization network, hydrogenation alters orbital occupations to shift preexisting Dirac points, originally embedded in the conduction bands, to the vicinity of the Fermi level in Cr$_2$Ge$_2$Te$_6$H$_6$. This electronic restructuring, coupled with spin-orbit coupling, opens a global topological gap of 118.1 meV, establishing a robust QAH state with Chern number $C=3$. Concurrently, this orbital reconstruction tunes the energy difference between the ligand $p$ and transition metal $d$ orbitals. This shift enhances ferromagnetic superexchange via the $d{z^2}-p_z-d_{xz}$ channel, strengthening the nearest-neighbor coupling $J_1$ by 3.06 times and switching $J_2$ from antiferromagnetic to ferromagnetic. Monte Carlo simulations based on extracted exchange parameters indicate a pronounced enhancement of ferromagnetic stability compared with pristine Cr$_2$Ge$_2$Te$_6$. While absolute Curie temperatures depend on the mapping to an effective spin model and represent relative trends, the enhanced stability after hydrogenation is a salient effect. This work establishes targeted orbital reconstruction driven by surface hydrogenation as a powerful route to simultaneously control topology and magnetism in 2D materials, providing a general route to engineer QAH phases with large gaps and high Chern numbers in van der Waals ferromagnetic semiconductors.