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

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 $4\times 4$ 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.

13 pages, 1 eps figure

References in corpus (10)

• Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
• Quantum Anomalous Hall State in Bilayer Graphene
• Quantum cascade of new correlated phases in trigonally warped bilayer graphene
• Cascade of isospin phase transitions in Bernal bilayer graphene at zero magnetic field
• Metal-insulator transition and phase separation in doped AA-stacked graphene bilayers
• AA-stacked bilayer graphene in an applied electric field: Tunable antiferromagnetism and coexisting exciton order parameter
• Phase separation of antiferromagnetic ground states in systems with imperfect nesting
• Gapped phase in AA stacked bilayer graphene
• Electronic Instabilities of the AA-Honeycomb Bilayer
• Antiferromagnetic ordering and excitonic pairing in the AA-stacked bilayer graphene

Cited by in corpus (3)

• Superconductivity and spin density wave in AA stacked bilayer graphene
• Ordered states in AB bilayer graphene in SU(4)-symmetric model
• Ordered states of undoped AB bilayer graphene: bias induced cascade of transitions