Emergent Quantum Valley Hall Insulator from Electron Interactions in Transition-Metal Dichalcogenide Heterobilayers

We explore the emergence of topological phases in moir\'{e} MoTe$_2$/WSe$_2$ bilayer, highlighting the crucial role of spin-orbit coupling and Coulomb interactions at two holes per moir\'e unit cell \(v = 2\). Our analysis uncovers robust Quantum Valley Hall Insulating (QVHI) 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 $p\pm ip$-$wave$ 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 (QAHI) state with the topological gap opening in a single valley and the other being topologically trivial.