To my surprise I found out that the flat bands of TMD heterobilayers automatically have a spin-orbit coupling that makes them realizations of the Kane-Mele model. This is different from the original Wu-MacDonald model where they say its a triangular lattice Hubbard model. Now on the arXiv!
Spin-Orbit Coupling in Transition Metal Dichalcogenide Heterobilayer Flat Bands
Louk Rademaker, arXiv:2111.06208
Abstract: The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.