Evidence for Flat Band Dirac Superconductor Originating from Quantum Geometry

Understand

In a flat band superconductor, the charge carriers' group velocity vF is extremely slow, quenching their kinetic energy.

• The emergence of superconductivity thus appears paradoxical, as conventional BCS theory implies a vanishing coherence length, superfluid stiffness, and critical current.
• Here, using twisted bilayer graphene (tBLG), we explore the profound effect of vanishingly small vF in a Dirac superconducting flat band system Using Schwinger-limited non-linear transport studies, we demonstrate an extremely slow vF ~ 1000 m/s for filling fraction nu 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.