Microwave Reflectometry for van der Waals 2D materials and heterostructures (Part-2): Superfluid stiffness of twisted trilayer graphene superconductors

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, a quantity that describes the energy required to vary the phase of the macroscopic quantum wave function. We report the measurement of superfluid stiffness in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of ρs at low temperatures and nonlinear Meissner effects in the current bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero temperature ρs and the superconducting transition temperature Tc, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.