Superfluid Stiffness and Flat-Band Superconductivity in Magic-Angle Graphene Probed by cQED

Abstract: The physics of superconductivity in magic-angle twisted bilayer graphene (MATBG) is a topic of keen interest in moir\'e systems research, and it may provide insight into the pairing mechanism of other strongly correlated materials such as high-$T_{\mathrm{c}}$ superconductors. Here, we use DC-transport and microwave circuit quantum electrodynamics (cQED) to measure directly the superfluid stiffness of superconducting MATBG via its kinetic inductance. We find the superfluid stiffness to be much larger than expected from conventional Fermi liquid theory; rather, it is comparable to theoretical predictions involving quantum geometric effects that are dominant at the magic angle. The temperature dependence of the superfluid stiffness follows a power-law, which contraindicates an isotropic BCS model; instead, the extracted power-law exponents indicate an anisotropic superconducting gap, whether interpreted within the Fermi liquid framework or by considering quantum geometry of flat-band superconductivity. Moreover, a quadratic dependence of the superfluid stiffness on both DC and microwave current is observed, which is consistent with Ginzburg-Landau theory. Taken together, our findings indicate that MATBG is an unconventional superconductor with an anisotropic gap and strongly suggest a connection between quantum geometry, superfluid stiffness, and unconventional superconductivity in MATBG. The combined DC-microwave measurement platform used here is applicable to the investigation of other atomically thin superconductors.