Hartree-Fock for symmetry-broken phases of rhombohedral N-layer graphene/hBN.

Rhombohedral N-layer graphene (RNG) aligned to an hBN substrate is a promising platform for interaction-driven topological phases. Recent experiments have revealed a variety of correlated and symmetry-broken states, including flavor-polarized insulators, anomalous Hall phases, and Chern insulators at zero magnetic field. Notably, pentalayer (N=5) and hexalayer (N=6) devices host robust anomalous Hall states and even fractional Chern insulators at zero external field. These systems also exhibit an unusual "single-gate tracking" behavior, where certain phase boundaries track a single gate voltage instead of remaining at a fixed displacement field. I develop a Hartree-Fock framework for RNG with N=3–6 layers that projects the interaction to the lowest minibands around the charge-neutrality point as well as incorporates an out-of-plane Hartree contribution to study symmetry-broken phases.