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Nontrivial interacting phases can emerge in elementary materials. As a primeexample, continuing advances in device quality have facilitated the observationof a variety of spontaneous quantum Hall-like states, a cascade of Stoner-likemagnets, and an unconventional superconductor in bilayer graphene. Its naturalextension, rhombohedral trilayer graphene is predicted to be even moresusceptible to interactions given its even flatter low-energy bands and largerwinding number. Theoretically, five spontaneous quantum Hall phases have beenproposed to be candidate ground states. Here, we provide transport evidence forobserving four of the five competing ordered states in interaction-maximized,dually-gated, rhombohedral trilayer graphene. In particular, at vanishing butfinite magnetic fields, two states with Chern numbers 3 and 6 can be stabilizedat elevated and low electric fields, respectively, and both exhibit clearmagnetic hysteresis. We also reveal that the quantum Hall ferromagnets of thezeroth Landau level are ferroelectrics with spontaneous layer polarizationseven at zero electric field, as evidenced by electric hysteresis. Our findingsexemplify the possible birth of rich interacting electron physics in a simpleelementary material.

Ferroelectric and anomalous quantum Hall states in bare rhombohedral trilayer graphene