Quantum anomalous Hall phenomena in multilayer rhombohedral graphene

The (fractional) quantum anomalous Hall effect observed in multilayer rhombohedral graphene raises many theoretical questions. I first show how the observed integer quantum anomalous Hall state at lattice filling \nu = 1 can be interpreted in terms of a valley polarized interaction-induced Chern band. The resulting many-body state can be viewed as a topological variant of the standard Wigner crystal, dubbed the `Anomalous Hall Crystal' (AHC), with a further coupling to a weak moiré potential. I will present a theoretical interpretation of the `extended' integer quantum anomalous Hall effect that persists over a wide range of density in terms of a crystal of holes doped into the \nu = 1 state. I show how the observed non-linear current-voltage curves at a generic filling as well as the current-induced transition to the Jain states at filling p/(2p+1) can be understood within this picture. Time permitting, I will also discuss the physics of Fractional Quantum Anomalous Hall states and proximate itinerant doped states. The latter includes both strongly time-reversal broken superconductivity and a charge oredred Fermi liquid metal.