We propose an alternative mechanism for the quantum anomalous Hall (QAH) effect in the $AB$ stacked $\mathrm{Mo}{\mathrm{Te}}_2/\mathrm{W}{\mathrm{Se}}_2$ system. Based on the observation that interlayer tunneling is suppressed in $AB$ stacking, we consider a model with two layers coupled through the Coulomb interaction. The moiré lattices of the two layers are shifted to form a honeycomb lattice. Initially, the system is in a layer-polarized Mott insulator at ${\nu }_T=1$. But with a displacement field, an equal number of holes and electrons are doped into the two layers, forming interlayer exciton condensation. Through mean field theory, we find $p\pm ip$ exciton condensation in a certain parameter regime, which leads to a Chern insulator with Chern number $\text{C}=\pm 1$. The valleys are polarized due to the kinetic energy instead of interaction, but the polarization in the two layers can be either the same or opposite. In particular, an intervalley-coherent (IVC) Chern insulator phase is possible, in agreement with the recent magnetic circular dichroism (MCD) measurement. Our work opens another direction in the search for a topologically nontrivial excitonic insulator with high angular momentum exciton pairing symmetry.

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• Excitons
• Topological insulators
• Topological phase transition
• Topological superconductors
• Strongly correlated systems
• Topological materials