Flat-band surface states and superconductivity in thick rhombohedral graphene

Rhombohedral multilayer graphene (RMG) has emerged as a rich platform for exploring correlation-driven quantum phenomena, including ferromagnetism, topological and superconducting states. While previous research has primarily focused on thin layer (M<10), a theoretical model that incorporates the electrostatics energy of charge redistribution across layer and the resultant non-linear layer-potential dependence, predicts a generic band structure for thicker RMG, featuring flat bands nearly perfectly polarized on the surface. Here, we investigate the thick RMG with M = 13~17, a regime where high energy subbands are irrelevant but the low energy band structure is nearly insensitive to layer number. We utilize a capacitive method to measure the gate capacitance between RMG and graphite gates, directly probing the layer polarization and revealing the existence of surface states. Intriguingly, these surfaces state generically host isospin symmetry-broken states, persist up to ~10K - almost one order of magnitude higher than in bilayer graphene (M=2), which we attribute to higher degeneracy of flat-bands. Proximate to the boundaries of the isospin symmetry-broken phase, we observe four distinct spin-polarized surface superconducting states. Remarkably, superconductivity can coexist on the top and bottom surface, paving the way for the study of crystalline Josephson junctions, in which the tunnel barrier is the pristine–and insulating–bulk of graphite. Our results reveal the surface states of bulk rhombohedral graphite as an highly reproducible platform for high temperature correlated electron physics.