Stripe and anomalous Hall orders in quarter metals of rhombohedral honeycomb multilayer

Motivated by recent experimental observations of two distinct phases in the valley and spin polarized quarter-metal in rhombohedral trilayer [Nat. Phys. 20, 1413 (2024)] and hexalayer [arXiv:2504.05129] graphene, here we identify the possibility of realizing a striped charge-density-wave (SCDW) order in the entire family of rhombohedral graphene heterostructures that can also be germane in monolayer and Bernal bilayer graphene. Besides the 3-fold rotational symmetry, this phase additionally breaks the translational symmetry and features a periodic modulation of charge density over an enlarged unit-cell with a characteristic 2K momentum, where K and -K are the valley momenta. Based on a Clifford algebraic symmetry argument, we establish that both the SCDW and an anomalous Hall order can lift the residual valley degeneracy of a spin-polarized half-metal, otherwise induced by the (layer) antiferromagnetic order when these systems are subject to external perpendicular displacement electric fields or a staggered sublattice potential (in monolayer graphene). However, only the anomalous Hall order shows a hysteresis in off-diagonal resistivity, as observed in all the multilayer systems. Finally, we showcase an intriguing confluence of the SCDW and anomalous Hall phases within the quarter metal phase in the mean-field approximation, generically manifesting a regime of coexistence between them, separating the pure phases.