Title: Superpolarized Electron-Hole Liquid and Multiferroicity in Multilayer Graphene

Abstract: 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 623, 41-47, 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 exhibits multiferroic order, characterized by spontaneous spin, layer, and valley polarization. We demonstrate the independent control of valley polarization and orbital magnetization in this state through the application of electric-displacement field and weak magnetic fields. The large magnetoelectric effect observed in the experiment is attributed to the substantial Berry curvature concentrated near the band edge. 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.