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arXiv · 2511.12231

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

Moru Song·Kai Chang
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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 topological transition that occurs in a regime signaled by a local geometric instability of the Bloch states. 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 becomes geometrically unstable and enters a Laughlin-$1/3$ phase within the same target $C=2$ manifold, which persists even as standard quantum-geometry indicators degrade further. We attribute this Laughlin-$1/3$ phase to a hidden near-ideal $C=1$ component of the non-ideal $C=2$ Bloch states that becomes relevant under interactions, while its strongly non-ideal partner becomes irrelevant. We support this picture by applying a weak perpendicular magnetic field that acts as a ``color separator,'' directly visualizing the ideal subcomponent at the single-particle level. Together, these results clarify how non-ideal flat bands can stabilize FCIs, greatly expanding their parameter range and sharpening the role of quantum geometry in strongly correlated topological phases.

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Moru Song, Kai Chang. 2025-11-15. Fractional Chern Insulators Transition in Non-ideal Flat Bands of Twisted Mono-bilayer Graphene. https://arxiv.org/abs/2511.12231

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