Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

Abstract

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.

arXiv comment20 pages, 11 figures, 2 tables

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• Reference results for the momentum space functional renormalization group
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• Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene
• Exotic charge density waves and superconductivity on the Kagome Lattice
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Loop Current Order on the Kagome Lattice
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Spin bond order driven by extended repulsive interactions in doped graphene