Nature of the fractional quantum spin Hall state in twisted $\mathrm{MoTe_2}$
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 three holes per moire cell, twisted $\mathrm{MoTe_2}$ near 2.1 degrees conducts along its edges with $3/2$ times the basic conductance quantum $e^{2}/h$ while keeping time-reversal symmetry (no preferred direction of time), and no accepted theory explains it.
Precise statement
Kang et al. (Nature 628, 522, 2024) reported in 2.1 deg twisted bilayer $\mathrm{MoTe_2}$ at hole filling $\nu = 3$ a state with vanishing Hall response and edge conductance near $\left(3/2\right)e^2/h$, interpreted as a fractional quantum spin Hall state, possibly a time-reversal pair of $3/2$ fractional Chern insulators. Identify its topological order (for example a time-reversal-symmetric non-Abelian state built from two Moore-Read halves, or an Abelian fractional topological insulator) and its edge theory, and determine whether the edge conductance is quantized. An answer is a topological order whose predicted edge conductance, quasiparticle charge and spin response match data.
What would settle it
Reproduction in independent devices plus edge shot-noise and nonlocal transport fixing the quasiparticle charge and edge-mode count.
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.
2024-2026 theory proposes non-Abelian spin Hall states (e.g., arXiv:2406.14617) and a 2026 preprint (arXiv:2601.18508) reports a fractional topological insulator candidate; the state is not identified.
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