Superconductivity and Ferroelectric Orbital Magnetism in Semimetallic Rhombohedral Hexalayer Graphene

Rhombohedral multilayer graphene has emerged as a promising platform for exploring correlated and topological quantum phases, enabled by its Berry-curvature-bearing flat bands. While prior work has focused on separated conduction and valence bands, we probe the extensive semimetallic regime of rhombohedral hexalayer graphene. We survey a rich phase diagram dominated by flavor-symmetry breaking and reveal an electric-field-driven band inversion through fermiology. Near this inversion, we find a superconducting-like state confined to a region with emergent electron and hole Fermi surfaces. In addition, two multiferroic orbital-magnetic phases are observed: a ferrovalley state near zero field and a ferroelectric state at large fields around charge neutrality. The latter shows electric-field-reversible magnetic hysteresis, consistent with a $ΔP \cdot M$ multiferroic order parameter. Our fermiology analysis elucidates the correlated semimetal regime in rhombohedral graphene and underscores its potential to host diverse quantum phases.