Fractional Chern Insulators Transition in Non-ideal Flat Bands of Twisted Mono-bilayer Graphene

Abstract

Fractional Chern insulators (FCIs) in ideal flat bands with Chern number $C$ are commonly understood as color-entangled states constructed from $C$ copies of the lowest Landau level. In realistic moir\'e systems, however, the band geometry is generally non-ideal, and the mechanism that stabilizes such FCIs remains unclear. Using twisted monolayer-bilayer graphene as a platform, we find two FCIs separated by a continuous transition driven by a geometric instability of the Bloch wave functions.Below the transition, the target $C=2$ conduction band is geometrically stable, and the resulting fractional phase is naturally described by the Halperin-$(112)$ state. Above the transition, the system is geometrically unstable, entering a Laughlin-$1/3$ phase that persists despite further degradation of standard quantum-geometry indicators. To account for this unconventional phenomenon, we propose a color-separation mechanism beyond global geometric indicators: in the geometrically unstable regime, interactions hybridize electronic states near the $K$ point and generate an emergent ideal color component that supports the FCI. We corroborate this picture by applying a weak perpendicular magnetic field that acts as a "color separator," directly visualizing the ideal subcomponent in the single-particle level. Together, these results establish mechanisms which non-ideal flat bands stabilize FCIs, substantially enlarging their viable parameter space and clarifying the role of quantum geometry in strongly correlated topological phases.