Quantitative test of geometric superfluid stiffness in moire superconductors
In plain words
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.
Precise statement
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.
What would settle it
Same-device measurement of $\Delta$ (tunnelling) and $D_{s}$ (kinetic inductance) compared with a calculation of the quantum metric of the interacting bands.
Status in the literature
Unverified 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.