ArXiv · 2025
Motivated by recent experiments, here we identify valley-coherent charge density wave (VC-CDW) in the nondegenerate quarter metal for the entire family of chirally-stacked n layer graphene, encompassing rhombohedral multilayer, Bernal bilayer, and monolayer cousins. Besides the hallmark broken translational symmetry, yielding a modulated charge density over an enlarged unit-cell with a characteristic 2bf K periodicity, where ± bf K are the valley momenta, this phase lacks the three-fold (C₃) rotational symmetry but only for n=1 and even integer n. The VC-CDW then represents a stripe order, as observed in hexalayer graphene [arXiv:2504.05129], but preserves the C₃ symmetry for other odd integer n as observed in trilayer graphene [https://www.nature.com/articles/s41567-024-02560-7Nat. Phys. bf 20, 1413 (2024) and arXiv:2411.11163]. From a universal Clifford algebraic argument, we show that the VC-CDW and an anomalous Hall order can lift the residual valley degeneracy of an antiferromagnetically ordered spin-polarized half metal, when these systems are subject to perpendicular displacement fields. Only the anomalous Hall order displays a hysteresis in off-diagonal resistivity, as observed in all the systems with 2 ≤ n ≤ 6. We showcase a confluence of VC-CDW and anomalous Hall orders within the quarter metal, generically displaying a regime of coexistence, otherwise separating the pure phases.
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