Discovery of Stable Multi-Band Fractional Chern Insulators in Rhombohedral Multilayer Graphene

We investigate fractional Chern insulators (FCIs) in a multi-band system of rhombohedral pentalayer graphene aligned with hexagonal boron nitride (hBN). Previous numerical studies of FCIs in this platform have mainly relied on restricted exact diagonalization (ED) within the lowest Hartree–Fock (HF) Chern band. However, when particles are allowed to occupy the higher bands, the FCI gap obtained from such single-band calculations typically collapses, calling into question the robustness of the state.

In this work, we develop a generalized criterion for identifying FCIs in multi-band systems, based on two key ingredients: the stability of the parent Chern-1 band and the effective interaction-induced bandwidth. We further introduce an iterative ED scheme that self-consistently optimizes the single-particle basis, ensuring that the particles in the many-body ground state predominantly occupy the lowest band.

Guided by these principles, we demonstrate that robust multi-band FCIs can persist despite substantial inter-band coupling. Our extensive multi-band ED simulations confirm that the FCI gap remains stable under large band mixing. We identify a crucial physical mechanism—the moiré-capacitor effect, in which Coulomb interactions with background charge density effectively enhance the moiré potential—as essential for stabilizing the FCI phase in this system.