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    Charge density waves and stripes in quarter metals of graphene heterostructures

    Sk Asrap Murshed and Bitan Roy*

    • *Contact author: bitan.roy@lehigh.edu

    Phys. Rev. B 114, 125412 – Published 14 August, 2026

    DOI: https://doi.org/10.1103/png3-tym5

    Abstract

    Motivated by recent experiments, here we identify the 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 2K periodicity, where ±K are the valley momenta, this phase lacks the threefold (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 [Nat. Phys. 20, 1413 (2024); 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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