Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moiré quantum materials at the forefront of condensed-matter research. In particular, bilayers of transition metal dichalcogenides (TMDs) have further enriched the opportunities for analysis and utilization of correlations in such systems. Recently, within the latter material class, the relevance of many-body interactions with an extended range has been demonstrated. Interestingly, the interaction, its range, and the filling can be tuned experimentally by twist angle, substrate engineering and gating.
Moiré hetero-bilayer TMDs can be accurately modelled by an effective extended Hubbard model on the triangular superlattice, which defines a starting point for quantum many-body approaches. In my presentation, I will discuss the Fermi surface instabilities and resulting correlated phases of hetero-bilayer TMDs employing a functional renormalization group approach with high momentum resolution. The results from this approach suggest that hetero-bilayer TMDs are unique platforms to realize topological superconductivity with high winding number which reflects in pronounced experimental signatures such as enhanced quantum Hall features.