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arXiv · 2306.05796

Ordering in SU(4)-symmetric model of AA bilayer graphene

A. V. Rozhkov·A. O. Sboychakov·A. L. Rakhmanov
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Abstract

We examine possible ordered states of AA stacked bilayer graphene arising due to electron-electron coupling. We show that under certain assumptions the Hamiltonian of the system possesses an SU(4) symmetry. The multicomponent order parameter is described by a $4\times4$ matrix $\hat{Q}$, for which a mean-field self-consistency equation is derived. This equation allows Hermitian and non-Hermitian solutions. Hermitian solutions can be grouped into three topologically-distinct classes. First class corresponds to the charge density wave. Second class includes spin density wave, valley density wave, and spin-valley density wave. An ordered state in the third class is a combination of all the aforementioned density-wave types. For anti-Hermitian $\hat{Q}$ the ordered states are characterized by spontaneous inter-layer loop currents flowing in the bilayer. Depending on the topological class of the solution these currents can carry charge, spin, valley, and spin-valley quanta. We also discuss the special case when matrix $\hat{Q}$ is not Hermitian and not anti-Hermitian. Utility and weak points of the proposed SU(4)-based classification scheme of the ordered states are analyzed.

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A. V. Rozhkov, A. O. Sboychakov, A. L. Rakhmanov. 2023-06-09. Ordering in SU(4)-symmetric model of AA bilayer graphene. https://doi.org/10.1103/physrevb.108.205153

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