Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices

Abstract: Recent experiments on pentalayer rhombohedral graphene moir\'e superlattices have observed the quantum anomalous Hall effect at moir\'e filling factor of $\nu = 1$ and various fractional values. These phenomena are attributed to a flat Chern band induced by electron-electron interactions. In this study, we demonstrate that at $\nu = 2$, many-body effects can lead to the emergence of quantum spin Hall and quantum valley Hall states, in addition to the quantum anomalous Hall state, even in the absence of spin-orbit coupling or valley-dependent potentials. These three topological states can be selectively induced by the application and manipulation of a magnetic field. Furthermore, we show that at $\nu = 3$ and $4$, the ground state can be a combination of topologically trivial and nontrivial states, unlike the cases of $\nu=1$ and 2. This contrasts with the conventional quantum Hall effect in graphene where the ground state at filling factor $\nu$ is given as the particle-hole counterpart at $4-\nu$.