{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"292b690126cd1c9c21c38141ec32e597908ad98bd35a159f5e1078455be8e6ae","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"acc528abf8caa8548830b2f44ff6507a2d37a6694bed013720b1f79c765503e2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.flat-band-geometry.geometric-stiffness-test","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Measurements since 2023 found that the superconducting pairs in magic-angle graphene are far stiffer than the slow electron speed allows, which points to quantum geometry, but a quantitative match to theory has not been made.","posed_since":"2015","precise":"For an isolated flat band with pairing gap $\\Delta$, mean-field theory gives a geometric superfluid weight $D_s^{\\mathrm{geom}}$ proportional to $\\Delta \\sqrt{\\nu_f (1 - \\nu_f)}$ times the Brillouin-zone integral of the quantum metric $g(k)$ ($\\nu_f$ the band filling fraction), bounded below by band topology. Compare the measured $D_s(T \\to 0)$ in magic-angle twisted bilayer and trilayer graphene with $D_s^{\\mathrm{geom}}$ computed from interaction-renormalized bands and the measured $\\Delta$. An answer is the ratio $D_s^{\\mathrm{meas}} / D_s^{\\mathrm{geom}}$ with uncertainty at several fillings.","problem_ref":null,"references":"","settled_by":"Same-device measurement of $\\Delta$ (tunnelling) and $D_{s}$ (kinetic inductance) compared with a calculation of the quantum metric of the interacting bands.","status_note":"Transport (Tian et al. 2023) and two 2025 Nature papers on twisted bilayer and trilayer graphene found $D_s$ about ten times the conventional estimate, consistent in magnitude with geometric contributions; a parameter-free comparison is lacking as of 2026.","title":"Quantitative test of geometric superfluid stiffness in moire 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