Is the moire potential needed for fractional anomalous Hall states?
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
In plain words
Fractional zero-field Hall states were found in pentalayer graphene aligned with boron nitride, but the electrons are on the layer far from the moire interface, so it is unclear whether the moire pattern matters.
Precise statement
In rhombohedral pentalayer (also tetralayer and hexalayer) graphene aligned to hBN, fractional quantum anomalous Hall (FQAH) states appear at moire fillings such as $\nu=2/3$ and $3/5$ under a displacement field $D$ that pushes electrons away from the aligned interface. Determine whether these are fractional Chern insulators of a moire-induced Chern band or interaction-driven anomalous Hall crystals that would survive with zero moire potential. An answer is FQAH observed in unaligned samples, or a quantitative theory giving the minimal moire strength required and matching the observed filling and $D$ windows.
What would settle it
Transport on matched aligned and unaligned devices, together with self-consistent calculations tested against the observed filling sequence and displacement-field windows.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Theory remains split between moire Chern-band and anomalous-Hall-crystal pictures; 2025-2026 experiments added FQAH states in tetralayer and new phase transitions (arXiv:2609.09422) without settling the question.
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