▎ 摘　　要

Recent experiments indicate that Bernal stacked graphene multilayers (BGMs) have an interaction-induced gapped (or pseudogapped) ground state. Here, we propose that, due to the electron correlation, the BGM can be induced into a half-metallic phase by applying a vertical electric field and doping. The half-metallic states in even-layer and odd-layer BGMs have totally different behaviors due to their different band structures. We systematically calculate the graphene tetralayer (4L-BGM) and trilayer (3L-BGM) as typical examples of even layer and odd-layer BGMs, respectively. In 4L-BGMs, we find an interesting phenomenon of electric field induced inversion of the spin-polarized bands, namely, in the half-metallic phase, the spin polarization of the conducting channel and the net magnetic moment are inversed when the applied electric field exceeds a critical value. In 3L-BGMs, a remarkable feature is that the inequivalence of the two sublattices will intrinsically break the degeneracy of the spin-up and spin-down bands even in the zero electric field case. Our results suggest that 4L-BGM could be an ideal platform to detect the proposed half-metallic phase in BGM systems.