Superfluid stiffness of twisted multilayer graphene superconductors

Abstract: The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, $\rho_s$, a quantity that describes the energy required to vary the phase of the macroscopic quantum wave function. In unconventional superconductors, such as cuprates, the low-temperature behavior of $\rho_s$ drastically differs from that of conventional superconductors due to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of $\rho_s$ to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of $\rho_s$ 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 $\rho_s$ 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 $\rho_s$ and the superconducting transition temperature $T_c$, 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.