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Remarkable recent experiments on the moir\'e structure formed by pentalayerrhombohedral graphene aligned with a hexagonal Boron-Nitride substrate reportthe discovery of a zero field fractional quantum hall effect. These``(Fractional) Quantum Anomalous Hall" ((F)QAH) phases occur for one sign of aperpendicular displacement field, and correspond, experimentally, to full orpartial filling of a valley polarized Chern-$1$ band. Such a band is absent inthe non-interacting band structure. Here we show that electron-electroninteractions play a crucial role, and present microscopic theoreticalcalculations demonstrating the emergence of a nearly flat, isolated, Chern-$1$band and FQAH phases in this system. We also study the four and six-layeranalogs and identify parameters where a nearly flat isolated Chern-$1$ bandemerges which may be suitable to host FQAH physics.

Theory of fractional quantum anomalous Hall phases in pentalayer rhombohedral graphene moir\'e structures