Ferroelectric and spontaneous quantum Hall states in intrinsic rhombohedral trilayer graphene

Non-trivial interacting phases can emerge in elementary materials. As a prime example, continuing advances in device quality have facilitated the observation of a variety of spontaneously ordered quantum states in bilayer graphene. Its natural extension, rhombohedral trilayer graphene—in which the layers are stacked in an ABC fashion—is predicted to host stronger electron–electron interactions than bilayer graphene because of its flatter low-energy bands and larger winding number. Theoretically, five spontaneous quantum Hall phases have been proposed to be candidate electronic ground states. Here we observe evidence for four of the five competing ordered states in interaction-maximized, dual-gated, rhombohedral trilayer graphene. In particular, at small magnetic fields, two states with Chern numbers 3 and 6 can be stabilized at elevated and low perpendicular electric fields, respectively, and both exhibit clear magnetic hysteresis. We also show that the quantum Hall ferromagnets of the zero-energy Landau levels are ferroelectrics with spontaneous layer polarizations even at zero electric field, as evidenced by electric hysteresis.