Topological $p_x+i{p}_y$ intervalley coherent state in moiré ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ heterobilayers

Recently, a quantum anomalous Hall (QAH) state was observed in AB-stacked moiré ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ heterobilayers at half filling. More recent layer-resolved magnetic circular dichroism measurements revealed that spin-polarized moiré bands from both the ${\mathrm{MoTe}}_2$ and the ${\mathrm{WSe}}_2$ layers are involved at the formation of the QAH state. This scenario is not expected by existing theories. In this work, we suggest that the observed QAH state is a new state of matter, namely, a topological $p_x+i{p}_y$ intervalley coherent state. We point out that the massive Dirac spectrum of the ${\mathrm{MoTe}}_2$ moiré bands, together with the Hund's interaction and the Coulomb interactions, gives rise to this novel QAH state. Through a self-consistent Hartree-Fock analysis, we study how this $p_x+i{p}_y$-pairing phase could appear. Besides explaining several key features of the experiments, our theory predicts that the order parameter would involve the pairing of electrons and holes with a definite momentum mismatch such that the pairing would generate a new unit cell which is three times the size of the original moiré unit cell, due to the order parameter modulations.