Stacking-Induced Large-Chern-Number Quantum Anomalous Hall Phases

We investigate the interaction between quantum anomalous Hall (QAH) phases hosted by two atomically thin hexagonal lattices and demonstrate the emergence of topological phases with large Chern numbers. Interlayer coupling between two graphene-like lattices produces band crossings, while relative sliding preserves gapless Dirac points located at generic, low-symmetry $\mathbf{k}$ points. The introduction of Haldane-type complex next-nearest-neighbor hoppings gaps these Dirac points, breaks time-reversal symmetry, and generates a sequence of quantum anomalous Hall phases. Depending on the phase angles $\phi_1$ and $\phi_2$ associated with the two layers, the system exhibits QAH states with Chern numbers $|C|>2$. The nontrivial bulk topology is verified by the presence of the corresponding number of chiral edge modes in ribbon geometries. These high-Chern-number phases originate from the enhanced twisting of the valence-band manifold induced by interlayer stacking.