Competing phases of interacting electrons on triangular lattices in moiré heterostructures

Abstract

We study the quantum many-body instabilities of interacting electrons with SU(2)$\times$SU(2) symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moiré heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions and analyze the different ordering tendencies with the help of an unbiased functional renormalization group approach. We find three classes of instabilities controlled by the filling and bare interactions. For a nested Fermi surface at van-Hove filling, Hund-like couplings induce a weak instability towards spin or orbital density wave phases. An SU(4) exchange interaction moves the system towards a Chern insulator, which is robust with respect to perturbations from Hund-like interactions or deviations from perfect nesting. Further, in an extended range of fillings and interactions, we find topological $d\pm id$ and (spin-singlet)-(orbital-singlet) $f$-wave superconductivity.

arXiv comment5+4 pages, 4+1 figures

References in corpus (43)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Exact evolution equation for the effective potential
• Observation of Van Hove singularities in twisted graphene layers
• Functional renormalization group approach to correlated fermion systems
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Localization of Dirac electrons by Moire patterns in graphene bilayers
• Chiral superconductivity from repulsive interactions in doped graphene
• Continuum Model of the Twisted Bilayer
• Evidence of Gate-Tunable Mott Insulator in Trilayer Graphene-Boron Nitride Moiré Superlattice
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Unravelling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene
• Topological Superconductivity in Twisted Multilayer Graphene
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Chiral SDW and d + id superconductivity in the magic-angle twisted bilayer-graphene
• Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
• Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene
• Phases of a phenomenological model of twisted bilayer graphene
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Chiral d-wave superconductivity in doped graphene
• Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
• Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moiré Superlattices
• Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice
• Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
• Charge-transfer insulation in twisted bilayer graphene
• Charge inversion and topological phase transition at a twist angle induced van Hove singularity of bilayer graphene
• Instabilities of interacting electrons on the triangular lattice
• Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
• Novel phases in twisted bilayer graphene at magic angles as a result of van Hove singularities and interactions
• Itinerant half-metal spin-density-wave state on the hexagonal lattice
• Spin-triplet $f$-wave pairing in twisted bilayer graphene near 1/4 filling
• Spontaneous quantum Hall effect in quarter-doped Hubbard model on honeycomb lattice and its possible realization in quarter-doped graphene system
• Kohn-Luttinger superconductivity on two orbital honeycomb lattice
• Symmetry analysis of translational symmetry broken density waves: application to hexagonal lattices in two dimensions
• Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice

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