Impact of spin-orbit coupling on superconductivity in rhombohedral graphene.

Spin-orbit coupling (SOC) has played an important role in many topological and correlated electron materials. In graphene-based systems, SOC induced by a transition metal dichalcogenide at close proximity has been shown to drive topological states and strengthen superconductivity. However, in rhombohedral multilayer graphene, a robust platform for electron correlation and topology, superconductivity and the role of SOC remain largely unexplored. Here we report transport measurements of transition metal dichalcogenide-proximitized rhombohedral trilayer graphene. We observed a hole-doped superconducting state SC4 with a critical temperature of 234 mK. On the electron-doped side, we noted an isospin-symmetry-breaking three-quarter-metal phase and observed that the nearby weak superconducting state SC3 is substantially enhanced. Surprisingly, the original superconducting state SC1 in bare rhombohedral trilayer graphene is strongly suppressed in the presence of transition metal dichalcogenide-opposite to the effect of SOC on all other graphene superconductivities. Our observations form the basis of exploring superconductivity and non-Abelian quasiparticles in rhombohedral graphene devices.