Why the zero-field $1/3$ state is weaker than the $2/3$ state
In plain words
In twisted MoTe2 the zero-field fractional Hall state at two thirds band filling is clear in transport while the one-third state is fragile or absent, the reverse of the ordinary fractional quantum Hall effect, where one third is the strongest.
Precise statement
In twisted bilayer MoTe2 at $\theta \sim 3.5-3.9\,\mathrm{deg}$, fractional quantum anomalous Hall states are seen in transport at hole fillings $\nu = -2/3$ and $-3/5$ of the first Chern band (Cai et al., Park et al., Zeng et al., Nature 2023), while at $\nu = -1/3$ only optical signatures of a fragile state over a narrow displacement-field range have been reported (arXiv:2602.04561). Explain this asymmetry: mixing with the second moire band, Berry-curvature and quantum-metric inhomogeneity, or interaction-induced band renormalization favouring a charge-density wave at $1/3$. An answer is a calculation with independently fixed parameters reproducing the ground state and gap at each filling and its displacement-field range.
What would settle it
Band-mixing-inclusive exact diagonalization or DMRG with independently fixed interaction parameters predicting the $\nu = -1/3$ ground state and gap, checked against transport and local imaging of charge order at that filling.
Status in the literature
Unverified note
Optical evidence for a fragile $-1/3$ state appeared in 2026 (arXiv:2602.04561); several 2023-2025 calculations point to band mixing and band renormalization, without consensus as of 2026, to this survey's knowledge.