{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0ca892a1fa335451598ff9da4febdd9ae19d6204aeb7b7812961880daddfd9e4","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","ee4f276fafa183e3382dbccfad4ec76ba8f4d210cd2b6d5b95a91ca34345474f"],"salt":"849e4bc81a5d6e14134b6f62ed1c5e82cc7e1f05b2a5b37f8642f59e2fe5a223","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.twisted-tmd.one-third-asymmetry","kind":"phenomenon","literature_status":"open","n":"2","parents":[],"plain":"In twisted $\\mathrm{MoTe_2}$ 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.","posed_since":"2023","precise":"In twisted bilayer $\\mathrm{MoTe_2}$ 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.","problem_ref":"ee4f276fafa183e3382dbccfad4ec76ba8f4d210cd2b6d5b95a91ca34345474f","references":"","settled_by":"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_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.","title":"Why the zero-field $1/3$ state is weaker than the $2/3$ 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