  Experimental demonstrations of tunable correlation effects in magic-angle
twisted bilayer graphene have put two-dimensional moir\'e quantum materials at
the forefront of condensed-matter research. Other twisted few-layer graphitic
structures, boron-nitride, and homo- or hetero-stacks of transition metal
dichalcogenides (TMDs) have further enriched the opportunities for analysis and
utilization of correlations in these systems. Recently, within the latter
material class, strong spin-orbit coupling or excitonic physics were
experimentally explored. The observation of a Mott insulating state and other
fascinating collective phenomena such as generalized Wigner crystals, stripe
phases and quantum anomalous Hall insulators confirmed the relevance of
many-body interactions, and demonstrated the importance of their extended
range. Since the interaction, its range, and the filling can be tuned
experimentally by twist angle, substrate engineering and gating, we here
explore Fermi surface instabilities and resulting phases of matter of
hetero-bilayer TMDs. Using an unbiased renormalization group approach, we
establish in particular that hetero-bilayer TMDs are unique platforms to
realize topological superconductivity with winding number $|\mathcal{N}|=4$. We
show that this state reflects in pronounced experimental signatures, such as
distinct quantum Hall features.
