Quantum anomalous Hall effect with tunable Chern numbers induced by d-wave sublattice-staggered altermagnetism

We construct a minimal spinful tight-binding model on a square lattice, where a $d$-wave sublattice-staggered altermagnetism drives the quantum anomalous Hall effect. Here the exchange field is staggered between the two sublattices, where it takes opposite signs on $A$ and $B$ described by the Pauli matrix $\tau_z$. The resulting insulating phases host tunable Chern numbers $\mathcal{C}=\pm1$ and $\mathcal{C}=\pm2$, controlled by the staggered exchange strength and the sublattice-staggered potential. We determine the complete phase diagram, identify valley-resolved band inversions at the $X$ and $Y$ points in the Brillouin zone, and demonstrate chiral edge states together with quantized two-terminal conductance plateaus. Our work provides a simple route to realizing the quantum anomalous Hall effect in compensated magnets via a $d$-wave sublattice-staggered altermagnetism.