Non-Abelian fractional state in a zero-field moire Chern band
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
Some predicted fractional states host non-Abelian anyons, quasiparticles whose exchange changes the system's state in an order-dependent way, and twisted $\mathrm{MoTe_2}$ may host one with no magnetic field.
Precise statement
Numerics predict Moore-Read-type non-Abelian order at half filling of a higher moire Chern band of twisted $\mathrm{MoTe_2}$ near $\theta \sim 2\ \mathrm{deg}$, a band whose wavefunctions resemble the first excited Landau level. Determine whether any zero-field moire Chern band hosts a gapped even-denominator state with non-Abelian order. An answer is a quantized even-denominator $\sigma_{xy}$ with $R_{xx} \to 0$ at $B = 0$, plus a half-integer chiral central charge from thermal Hall or $e/4$ quasiparticle charge.
What would settle it
Zero-field transport showing an even-denominator quantized Hall plateau, followed by thermal Hall or shot-noise measurements of e/4 charge.
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.
Predicted in 2024 numerics (e.g., arXiv:2405.08386); the $\nu = 3$ fractional spin Hall state (Kang et al. 2024) may be a time-reversal pair of $3/2$ states, but no quantized even-denominator $\sigma_{xy}$ at $B = 0$ has been observed as of 2026.
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