{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1d47f8ea8a2656d6b33547a1f569ad36fb14acac29871f06a884f191287bb805","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["69afa9fbcd1de23920428803e8538fb40733550a31ec3f4256640b9c953a2dff","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"19cf0f06d58c357461302c11e1a786ef8e0361bb7b21ba4579d9c45ab9f02fc5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"cm.moire-graphene-superconductivity.isotope-effect","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Replacing carbon-12 by heavier carbon-13 slows the lattice vibrations, and the resulting shift of the superconducting transition temperature, compared with what each pairing theory predicts, would test whether phonons bind the pairs.","posed_since":"","precise":"For magic-angle devices built from 13C-enriched graphene, measure the isotope coefficient $\\alpha_{\\mathrm{iso}} = -d \\ln T_c / d \\ln M$ at fixed twist angle, filling and heterostrain, and compare it with the value each candidate mechanism predicts. For pairing by K-point optical phonons ($\\hbar \\omega \\sim 0.15\\,\\mathrm{eV}$ $>> \\text{ flat-band width}$ $W \\sim 10\\,\\mathrm{meV}$) the anti-adiabatic regime can give $\\alpha_{\\mathrm{iso}}$ well below the BCS value 0.5; a purely electronic mechanism gives $\\alpha_{\\mathrm{iso}} \\sim 0$. Since $\\ln(13/12) = 0.08$, the answer is $\\alpha_{\\mathrm{iso}}$ with an error bar small enough to separate the computed predictions, which requires a statistical ensemble of devices.","problem_ref":"69afa9fbcd1de23920428803e8538fb40733550a31ec3f4256640b9c953a2dff","references":"","settled_by":"Transport $T_c$ measured on ensembles of 12C and 13C magic-angle devices with matched angle and strain and quantified sample-to-sample scatter, compared with mechanism-specific calculations of $\\alpha_{\\mathrm{iso}}$ in the flat-band regime.","status_note":"No measurement on isotope-enriched magic-angle devices is known to this survey as of 2026.","title":"Carbon isotope effect on the magic-angle superconducting transition temperature","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ebec8fd68fcf217fc1e2f3470dffdfe6d949a4694f5082b85058b4181c8031ca","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"47a4936aa8d58b934407b3e0ce930eca2904e85efc64a11570c46b97e9d316ef","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"iV8xEeAbVlhke6QR28CsHEhl2WQNe1GJM2hjjB9Kj_ExeqwB7F8IfBgxJTSGGnR9IdfLaCu68GWVHBkQ21AsBQ"},"schema":"pubphys.envelope/1"},"record_hash":"ebec8fd68fcf217fc1e2f3470dffdfe6d949a4694f5082b85058b4181c8031ca","leaf_index":2948}