Evidence for Flat Band Dirac Superconductor Originating from Quantum Geometry

TL;DR

This paper investigates flat band superconductivity in twisted bilayer graphene, revealing extremely slow charge carrier velocities, a quantum geometric contribution to superfluid stiffness, and evidence for BCS-BEC crossover in a strongly coupled system.

Contribution

It demonstrates the role of quantum geometry in superfluid stiffness and provides experimental evidence for ultra-strong coupling superconductivity with BCS-BEC crossover characteristics.

Findings

Charge carrier velocity vF ~ 1000 m/s in flat bands.

Superfluid stiffness dominated by interaction-driven gap, not kinetic energy.

Superconducting T_c/Fermi temperature ratio exceeds unity, indicating strong coupling.

Abstract

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. 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. We find evidence for small pairs, characteristic of the BCS to Bose-Einstein condensation (BEC) crossover, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity, and discuss how this arises for very strong coupling superconductivity in ultra-flat Dirac bands.