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In a flat band superconductor, the charge carriers' group velocity vF isextremely slow, quenching their kinetic energy. The emergence ofsuperconductivity thus appears paradoxical, as conventional BCS theory impliesa vanishing coherence length, superfluid stiffness, and critical current. Here,using twisted bilayer graphene (tBLG), we explore the profound effect ofvanishingly small vF in a Dirac superconducting flat band system UsingSchwinger-limited non-linear transport studies, we demonstrate an extremelyslow vF ~ 1000 m/s for filling fraction nu between -1/2 and -3/4 of the moiresuperlattice. In the superconducting state, the same velocity limit constitutesa new limiting mechanism for the critical current, analogous to a relativisticsuperfluid. Importantly, our measurement of superfluid stiffness, whichcontrols the superconductor's electrodynamic response, shows that it is notdominated by the kinetic energy, but instead by the interaction-drivensuperconducting gap, consistent with recent theories on a quantum geometriccontribution. We find evidence for small pairs, characteristic of the BCS toBose-Einstein condensation (BEC) crossover, with an unprecedented ratio of thesuperconducting transition temperature to the Fermi temperature exceedingunity, and discuss how this arises for very strong coupling superconductivityin ultra-flat Dirac bands.

Evidence for Flat Band Dirac Superconductor Originating from Quantum Geometry