Nature of the fractional quantum spin Hall state in twisted MoTe2
In plain words
At three holes per moire cell, twisted MoTe2 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 MoTe2 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
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.