Rhombohedral Multilayer Graphene as a $p$-Wave Magnet

Abstract

We propose rhombohedral multilayer graphene in an applied in-plane magnetic field as a highly tunable platform for nonrelativistic collinear $p$-wave magnetism. The orbital coupling to the magnetic field breaks time-reversal symmetry and, together with interaction-driven layer antiferromagnetism, generates an odd-in-momentum spin splitting without relying on spin-orbit coupling. Using a minimal low-energy effective theory, we show that the resulting $p$-wave spin splitting is strongly enhanced with increasing layer number. This enhancement originates from the surface-localized nature of the low-energy states and their layer-dependent orbital coupling to the in-plane field. The Zeeman coupling only weakly perturbs this predominantly orbital-field-induced mechanism. We further estimate stability of the $p$-wave magnetism under hole-doping and distinct transport signature using a more realistic Hubbard model. Our results establish orbital coupling to an external magnetic field as a controllable route to odd-parity spin splitting in collinear magnets.