Evidence for Dirac flat band superconductivity enabled by quantum geometry.

In a flat band superconductor, the charge carriers' group velocity v F is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors 1 and heavy-fermion systems 2 . Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small v F in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene 3-7 , we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system 8-13 . Using Schwinger-limited non-linear transport studies 14,15 , we demonstrate an extremely slow normal state drift velocity v n  ≈ 1,000 m s -1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid 16 . Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution 8-12 . We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover 17-19 , with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.