{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"774c8c3a769ad342ab43dc2d7061c55a900fe9e511516e8522cc061907a2d7cd","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["0f6f53bee804850e42ae1bef3cd6e630563805426f86098340ea94f854a7a1c8","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"803314a179a17f3353c06411790d08b6da4710d0b2fc904265bca1d6960c628a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"cm.flat-band-geometry.linear-tc-scaling","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"For flat bands theory predicts a superconducting temperature proportional to the pairing attraction, much larger than the exponentially small value of ordinary metals when the attraction is weak, and no experiment has tested this scaling directly.","posed_since":"2011","precise":"For an isolated flat band of width $W \\ll U$ ($U$ the effective attraction), mean-field and Berezinskii-Kosterlitz-Thouless theory predict $T_c \\sim U$ times a band-geometric factor, compared with $T_c \\sim W \\exp(-1/(N(0) U))$ in dispersive bands, $N(0)$ the density of states. Determine whether $T_c$ scales linearly with $U$ in a moire flat-band superconductor where the interaction is tuned, for example by gate-screening distance or dielectric environment. An answer is the measured exponent of $T_c$ versus $U$.","problem_ref":"0f6f53bee804850e42ae1bef3cd6e630563805426f86098340ea94f854a7a1c8","references":"","settled_by":"$T_{c}$ measured versus screening-layer distance or dielectric environment in moire devices with independently estimated $U$ and fixed band structure.","status_note":"","title":"Linear scaling of $T_c$ with attraction in isolated flat bands","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5202f65a1abae43173d3e60653e2fdc86a228aa334f7d44a97c6c056cad37883","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"e25c94a4770b7eee8e3e0ce489556988712acd155499be4b6c76f268ef4c3058","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"fE45aK06cMLBhPaQJJSen5vLA2WbV9nf3EhhlQbUw9F8QlDth2d_U8o7al-nWtRvnm-Yt5A28goOz1fXoOivDA"},"schema":"pubphys.envelope/1"},"record_hash":"5202f65a1abae43173d3e60653e2fdc86a228aa334f7d44a97c6c056cad37883","leaf_index":2804}