Superfluid stiffness of magic-angle twisted bilayer graphene

The physics of superconductivity in magic-angle twisted bilayer graphene (MATBG) is a topic of keen interest in moir & eacute; systems research, and it may provide an insight into the pairing mechanism of other strongly correlated materials such as high-critical-temperature superconductors. Here we use d.c. transport and microwave circuit quantum electrodynamics to directly measure the superfluid stiffness of superconducting MATBG through 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 predictions1 and recent experimental indications2 of 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 Bardeen-Cooper-Schrieffer (BCS) model. Instead, the extracted power-law exponents indicate an anisotropic superconducting gap, whether interpreted in the Fermi liquid framework or by considering the quantum geometry of flat-band superconductivity. Moreover, a quadratic dependence of the superfluid stiffness on both d.c. and microwave current is observed, which is consistent with the Ginzburg-Landau theory. Taken together, our findings show 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 d.c.-microwave measurement platform used here is applicable to the investigation of other atomically thin superconductors.