A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene

Abstract

We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

7 + 11 pages, 4 + 2 figures; (v2) 5 + 12 pages, 4 + 3 figures, added figures and references; (v3) 5 + 13 pages, minor changes, added a comment on Landau fans. Published version

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• Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing
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• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
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• Ballistic miniband conduction in a graphene superlattice
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• A chiral twist on the high-$T_c$ phase diagram in Moiré heterostructures
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• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
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• Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
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• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene
• Band structure of twisted bilayer graphene on hexagonal boron nitride
• Heavy fermion representation for twisted bilayer graphene systems
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• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
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• Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene
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• Spin-Orbit Coupling in Transition Metal Dichalcogenide Heterobilayer Flat Bands
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• Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition
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• Josephson effect in graphene bilayers with adjustable relative displacement
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• Intrinsically-multilayer moiré heterostructures
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• Linear Magnetoresistance from Glassy Orders
• Exact ground state of interacting electrons in magic angle graphene
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• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
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• Signatures of electronic ordering in transport in graphene flat bands
• Lattice Model For The Quantum Anomalous Hall Effect in Moiré Graphene
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
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• Topological phase transition from periodic edge states in moiré superlattices
• Nonreciprocal Current-Induced Zero-Resistance State in Valley-Polarized Superconductors
• Twisted Nodal Superconductors
• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• Collective excitations of the Chern-insulator states in commensurate double moiré superlattices of twisted bilayer graphene on hexagonal boron nitride
• Theory for Lattice Relaxation in Marginal Twist Moirés
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
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