Quantitative test of geometric superfluid stiffness in moire superconductors · revision history
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Accepted · first revision · record
- Title
- Quantitative test of geometric superfluid stiffness in moire superconductors
- 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.
- 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.
- 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.
- Kind
- well-posed
- Answer type
- value
- References
- (empty)
- Literature status
- partially-resolved
- 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.
- Posed since
- 2015