Chiral twist on the high-T_c phase diagram in moiré heterostructures

We show that the large orbital degeneracy inherent in moiré heterostructures naturally gives rise to a 'high-T_c' like phase diagram with a chiral twist - wherein an exotic quantum anomalous Hall insulator is flanked by chiral d+id superconducting domes. Specifically, we analyze repulsively interacting fermions on hexagonal lattices near Van Hove filling, with an SU(4) flavor degeneracy. At this point, a nested Fermi surface and divergent density of states give rise to strong ln² instabilities to correlated phases, the competition between which can be controllably addressed through a combination of weak coupling parquet renormalization group and Landau-Ginzburg analysis. We uncover an unambiguous and rich behavior, wherein at weak coupling the leading instability is to a Chern insulator, characterized by a spontaneous breaking of time reversal symmetry and a quantized Hall response. Upon doping this phase gives way to a chiral d+id superconductor. We further consider deforming this minimal model by an orbital splitting, and discuss the resulting RG flow and phase diagram. Our analysis thus bridges the minimal model and the practical moiré bands, thereby elucidates transparently how the correlated phases arise.