Kohn-Luttinger superconductivity on two orbital honeycomb lattice

Abstract

Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\text{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pairing instability further has a twelve-fold degeneracy while the $f$-wave pairing instability has a ten-fold degeneracy. We analyze the symmetry breaking perturbations to this model. Combining this with a Ginzburg-Landau analysis, we conclude that close to Van Hove filling, a spin singlet $d+id$ pairing state should form (consistent with several other investigations of twisted bilayer graphene), whereas away from Van Hove filling we propose an unusual spin and orbital singlet $f$-wave pairing state.

arXiv comment10 pages, 3 figures. v3: Published version

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• Nematic superconductivity in twisted bilayer graphene
• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Competing orders at higher-order Van Hove points
• Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene
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• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Light-matter coupling and quantum geometry in moiré materials
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• Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene
• Spin-valley density wave in moiré materials
• Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone
• Unconventional superconductivity due to interband polarization
• Superconductor versus insulator in twisted bilayer graphene
• Multidome superconductivity in charge density wave kagome metals
• Correlation-induced triplet pairing superconductivity in graphene-based moiré systems
• Degradation of phonons in disordered moiré superlattices
• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Nematic, chiral and topological superconductivity in transition metal dichalcogenides
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene
• Moiré Flat Bands of Twisted Few-layer Graphite
• Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene
• High-$T_{\text{C}}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\acute{e}$ Superlattices
• Extended linear-in-$T$ resistivity due to electron-phason scattering in moiré superlattices
• Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields
• Renormalization-group approach to the Kohn-Luttinger superconductivity: Amplification of the pairing gap from ${\ell }^4$ to $\ell$
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• Triplet superconductivity supported by an X${}_9$ high-order Van Hove singularity