Charge-density waves and stripes in quarter metals of graphene heterostructures

TL;DR

This paper identifies valley-coherent charge-density wave order in quarter-metals of layered graphene, revealing symmetry-breaking patterns, coexistence with anomalous Hall order, and explaining experimental observations across various graphene multilayers.

Contribution

It introduces the concept of valley-coherent charge-density wave order in quarter-metals of chirally-stacked graphene and analyzes its symmetry properties and coexistence with anomalous Hall order.

Findings

VC-CDW order causes translational symmetry breaking with a 2K periodicity.

Stripe order varies with the parity of the number of layers, preserving C3 symmetry for odd n.

Coexistence of VC-CDW and anomalous Hall order explains resistivity hysteresis.

Abstract

Motivated by recent experiments, here we identify valley-coherent charge-density wave (VC-CDW) order in the non-degenerate quarter-metal for the entire family of chirally-stacked $n$ layer graphene, encompassing rhombohedral multi-layer, Bernal bilayer, and monolayer cousins. Besides the hallmark broken translational symmetry, yielding a modulated charge-density over an enlarged unit-cell with a characteristic $2{\bf K}$ periodicity, where $\pm {\bf K}$ are the valley momenta, this phase lacks the three-fold ($C_3$) rotational symmetry but only for even integer $n$. The VC-CDW then represents a stripe order, as observed in hexalayer graphene [arXiv:2504.05129], but preserves the $C_3$ symmetry for odd $n$ as observed in trilayer graphene [Nat. Phys. 20, 1413 (2024) and arXiv: 2411.11163]. From a universal Clifford algebraic argument, we establish 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, with only the latter one displaying a hysteresis in off-diagonal resistivity, as observed in all the systems with $2 \leq n \leq 6$. We showcase a confluence of VC-CDW and anomalous Hall orders within the quarter-metal, generically displaying a regime of coexistence, separating the pure phases.