{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6d67f1f78ee04518906f002de5cc3d5aab90d811892146b62a5012b2dd70daf0","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["4e26afc00b7011defe0fb8dd7e4edec02af962c3bb628d77fb25bedb149ad4e3","5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5a8e8866dc8b8454a1153a784666b518e55af41f07ce133623e967c3f775be85","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.moire-graphene-superconductivity.isotope-effect","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"4e26afc00b7011defe0fb8dd7e4edec02af962c3bb628d77fb25bedb149ad4e3","relation":"special_case"}],"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 ($\\hbar \\omega \\sim 0.15\\,\\mathrm{eV}$ >> flat-band width $W \\sim 10\\,\\mathrm{meV}$) the anti-adiabatic regime can give alpha_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":null,"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 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