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 upsilon between -1/2 and -3/4 of the moire 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.