We explore the emergence of topological phases in moiré ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ bilayer, highlighting the crucial role of spin-orbit coupling and Coulomb interactions at two holes per moiré unit cell $v=2$. Our analysis uncovers robust quantum valley Hall insulating phase and reveals that long-range interactions alone can mediate the interlayer electron tunneling, generating topologically nontrivial bands even in the absence of the corresponding single-particle hopping. Additionally, we show that in the case of band mixing terms originating both from the interaction and single-particle physics, a competition between topological states realizing $s$-wave and $(p\pm ip)\text{-wave}$ symmetries can appear. Moreover, within the considered theoretical framework, we present that by introducing a small Zeeman field, one can lift the band inversion in one of the valleys. This leads to a quantum anomalous Hall insulating state with the topological gap opening in a single valley and the other being topologically trivial.

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• Flat bands
• Twistronics
• Valley degrees of freedom
• 2-dimensional systems
• Topological insulators
• Topological materials
• Transition metal dichalcogenides
• Twisted heterostructures