Theory of Quantum Anomalous Hall Phases in Pentalayer Rhombohedral Graphene Moiré Structures

Remarkable recent experiments on the moir\'e structure formed by pentalayer rhombohedral graphene aligned with a hexagonal boron nitride substrate report the discovery of a zero field fractional quantum Hall effect. These ``(fractional) quantum anomalous Hall'' [(F)QAH] phases occur for one sign of a perpendicular displacement field, and correspond, experimentally, to full or partial filling of a valley polarized Chern-1 band. Such a band is absent in the noninteracting band structure. Here we show that electron-electron interactions play a crucial role, and present microscopic theoretical calculations demonstrating the emergence of a nearly flat, isolated, Chern-1 band and FQAH phases in this system. We also study the four- and six-layer analogs and identify parameters where a nearly flat isolated Chern-1 band emerges which may be suitable to host FQAH physics.