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Of the two stable forms of graphite, hexagonal (HG) and rhombohedral (RG),the former is more common and has been studied extensively. RG is less stable,which so far precluded its detailed investigation, despite many theoreticalpredictions about the abundance of exotic interaction-induced physics. Advancesin van der Waals heterostructure technology have now allowed us to makehigh-quality RG films up to 50 graphene layers thick and study their transportproperties. We find that the bulk electronic states in such RG are gapped and,at low temperatures, electron transport is dominated by surface states. Becauseof topological protection, the surface states are robust and of high quality,allowing the observation of the quantum Hall effect, where RG exhibits phasetransitions between gapless semimetallic phase and gapped quantum spin Hallphase with giant Berry curvature. An energy gap can also be opened in thesurface states by breaking their inversion symmetry via applying aperpendicular electric field. Moreover, in RG films thinner than 4 nm, a gap ispresent even without an external electric field. This spontaneous gap openingshows pronounced hysteresis and other signatures characteristic of electronicphase separation, which we attribute to emergence of strongly-correlatedelectronic surface states.

Electronic phase separation in topological surface states of rhombohedral graphite