Microscopic theory of multiferroic behavior in rhombohedral multilayer graphene

We introduce a many-body state termed superpolarized electron-hole liquid to explain the multiferroic properties observed in a recent experiment on rhombohedral pentalayer graphene by Han et al. [Nature (London) 623, 41 (2023)]. Superpolarization refers to a state where electrons and holes are fully polarized in opposite directions within the extended spin-valley space, resulting in a polarization per charge that exceeds the saturated value of one. This state is characterized by triferroic order, exhibiting spontaneous polarization in spin, layer, and valley degrees of freedom. Specifically, layer polarization creates spontaneous electric dipole moments oriented perpendicular to the two-dimensional material stack, while valley polarization represents of momentum space condensation. The presence of this triferroic order allows a time-reversal even electric displacement field to induce a time-reversal breaking response, manifesting as the anomalous Hall effect. We also detail how valley polarization and orbital magnetization can be independently controlled through the experimental parameter space of electric displacement and magnetic fields. The concept of superpolarization can be probed experimentally through magnetic oscillation and local current distribution measurements to determine the area of the Fermi surfaces and their magnetic moments.