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The experimental discovery of fractional Chern insulators (FCIs) inrhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) haspreceded theoretical prediction. Supported by large-scale first principlesrelaxation calculations at the experimental twist angle of $0.77^\circ$, weobtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedralgraphene-hBN moir\'e systems. Focusing on the pentalayer case, we analyticallyexplain the robust $|C|=0,5$ Chern numbers seen in the low-energysingle-particle bands and their flattening with displacement field, making useof a minimal two-flavor continuum Hamiltonian derived from the full model. Wethen predict nonzero valley Chern numbers at the $\nu = -4,0$ insulatorsobserved in experiment. Our analysis makes clear the importance of displacementfield and the moir\'e potential in producing localized "heavy fermion" chargedensity in the top valence band, in addition to the nearly free conductionband. Lastly, we study doubly aligned devices as additional platforms formoir\'e FCIs with higher Chern number bands.

Moir\'e Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices