Nature of the extended quantum anomalous Hall state
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
At the lowest temperatures pentalayer graphene shows an integer quantized Hall resistance over a wide range of electron densities, replacing the fractional states, and the electronic structure behind it is unknown.
Precise statement
Lu et al. (Nature 637, 1090, 2025; arXiv:2408.10203) reported an extended integer quantum anomalous Hall state, $R_{xy} = h/e^{2}$ with vanishing $R_{xx}$ over a continuous range of moire filling from $\nu \sim 0.5$ to $\sim 1.3$, appearing at the lowest temperatures in rhombohedral pentalayer graphene/hBN. Identify the state: an anomalous Hall crystal (electron crystal with Chern number 1) pinned by disorder, a moire-commensurate state, or another order. An answer determines whether translation symmetry is broken and how the crystal period varies with density.
What would settle it
Local imaging (STM or scanning single-electron transistor) of a density-dependent crystal period coexisting with quantized Hall response.
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.
Interpretation as an anomalous Hall crystal is not confirmed by imaging as of 2026.
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