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

Phys. Rev. B 109, 205122 (2024) The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moir\'e systems. Focusing on the pentalayer case, we analytically explain the robust $|C|=0,5$ Chern numbers seen in the low-energy single-particle bands and their flattening with displacement field, making use of a minimal two-flavor continuum Hamiltonian derived from the full model. We then predict nonzero valley Chern numbers at the $\nu = -4,0$ insulators observed in experiment. Our analysis makes clear the importance of displacement field and the moir\'e potential in producing localized "heavy fermion" charge density in the top valence band, in addition to the nearly free conduction band. Lastly, we study doubly aligned devices as additional platforms for moir\'e FCIs with higher Chern number bands.