Superconductivity from repulsion in a single-flavor graphene band
In plain words
In a band where all electrons share one spin and one valley (one of graphene's two momentum regions for low-energy electrons), pairs must have odd symmetry, and whether the electrons' own repulsion can produce such pairing at the observed temperature is unsettled.
Precise statement
For a spin- and valley-polarized rhombohedral graphene band at $n \sim 1e11-1e12\,\mathrm{cm}^{-2}$ with gate-screened Coulomb interaction, compute the odd-parity pairing $T_c$ from Kohn-Luttinger, Berry-curvature-enhanced or order-parameter-fluctuation mechanisms and compare with phonon-mediated odd-parity pairing. An answer is a calculation reproducing $T_c \sim 0.1-0.3\,\mathrm{K}$ and its density and displacement-field window.
What would settle it
A quantitative calculation matching measured $T_{c}(n, D)$, tested by the predicted dependence on gate-to-sample distance in devices with different gate spacings.