Magnetic imaging of superconductivity in rhombohedral tri-layer graphene

Rhombohedral graphene multilayers exhibit rich correlated phase diagrams, revealing a complex interplay between superconductivity and isospin magnetism. Magnetic imaging of superconductors can provide detailed quantitative and qualitative information about the superconducting states, including the standard diamagnetic response from vortices as well as signatures of time-reversal-symmetry breaking that may accompany spontaneous chiral superconductivity. However, such measurements are experimentally demanding in graphene superconductors due to the exceptionally low-carrier density and resulting screening currents.

Here we use ultra-low temperature magnetometry to image the magnetic fringe fields onsetting at the superconducting transition temperature in rhombohedral trilayer graphene with proximity enhanced spin orbit coupling. While the isospin phase diagram closely resembles that of bare RTG, a superconducting phase with Tc = 300 mK emerges at the low-displacement-field boundary of a half-metal phase. Utilizing a nano-SQUID-on-tip sensor operating at zero applied out-of-plane magnetic field in a dilution refrigerator, we observe a faint magnetic fringe field that appears spontaneously upon entering the superconducting state. The amplitude of this fringe field is nearly independent of the applied out-of-plane magnetic field and has a highly inhomogeneous, sign-changing spatial distribution. We discuss these results in light of current theoretical models for the superconducting state in these systems.