Evidence for Dirac flat band superconductivity enabled by quantum geometry

In a flat band superconductor, the charge carriers’ group velocity vF is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors1 and heavy-fermion systems2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small vF in the conventional Bardeen–Cooper–Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene3–7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system8–13. Using Schwinger-limited non-linear transport studies14,15, we demonstrate an extremely slow normal state drift velocity vn ≈ 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 superfluid16. 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 contribution8–12. We find evidence for small Cooper pairs, characteristic of the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover17–19, 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.