Measurement of Superfluid Stiffness of Twisted Multilayer Graphene Superconductors

The response of a superconductor to external fields is characterized by its superfluid rigidity, a measure of the energy required to change the phase of the macroscopic quantum wave function. Unlike conventional superconductors, where this property behaves predictably at low temperatures, unconventional superconductors, such as high-temperature cuprate superconductors, exhibit a distinct behavior due to quasiparticle excitations from gapless points (nodes) in momentum space. Recent studies on the magnetically twisted graphene family have revealed not only superconducting states, but also strongly correlated electronic states associated with spontaneously broken symmetries, sparking interest in measuring superfluid stiffness to better understand the potentially unconventional superconductivity these materials may exhibit. In this talk, we will discuss superfluid stiffness measurements in magic-angle twisted trilayer graphene (TTG) that reveal unconventional node-gap superconductivity. Using high-frequency reflectometry to assess the kinetic-inductive response of superconducting TTG coupled to a microwave resonator, we observe a linear temperature dependence at low temperatures and nonlinear Meissner effects in the current bias, both of which are indicative of nodal structures in the superconducting order parameter. In addition, we find a linear relationship between the zero-temperature superfluid stiffness and the superconducting transition temperature, reminiscent of Uemura's relationship in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide compelling evidence for nodal superconductivity in TTG and place significant constraints on the possible mechanisms driving superconductivity in these graphene-based materials.