Chiral superconductivity from a parent Chern band and its non-Abelian generalization

We propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetralayer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose--Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose--Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multilayer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the nonabelian Moore--Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore--Read quantum Hall phase. Our work suggests rhombohedral multilayer graphene as a potential platform for rich correlated topological phases.