Magnetism and superconductivity in rhombohedral graphene multilayers: triplet superconductivity, intervalley coherence, and spin orbit coupling

The noninteracting band structure of rhombohedral graphene multilayers is characterized by displacement field tunable van Hove singularities where the single particles density of states diverges. When the system is doped into the center of these singularities, a variety of interaction driven instabilities are observed, including magnetic and superconducting states are observed. Crucially, rhombohedral graphene multilayers can be fabricated with low disorder and high reproducibility. This allows carefully controlled experiments to probe both the interplay of intrinsic symmetry breaking terms as well as extrinsic substrate effects such as a periodic potential or enhanced spin orbit coupling. I will review experiments on these systems, focusing on experimental constraints imposed on the ground state phase diagram by transport, magnetization, and compressibility measurements in rhombohedral trilayer graphene.