Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

Abstract

We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading inter-valley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong coupling approaches, indicating that this order is robust. The other is a mixed state with $120^{\circ }$ complex spin order and orthogonal complex charge order. In addition, we find a weaker, but still attractive interaction in nematic channels, and discuss the type of a nematic order.

15 figures, 48 pages. Version accepted by Phys. Rev. B

References in corpus (3)

• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe

Cited by in corpus (22)

• Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Altermagnetism from interaction-driven itinerant magnetism
• SU(4) symmetry in twisted bilayer graphene - an itinerant perspective
• Superconductivity from Orbital-Selective Electron-Phonon Coupling in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$
• Current Switching of Valley Polarization in Twisted Bilayer Graphene
• Cascade of transitions in twisted and non-twisted graphene layers within the van Hove scenario
• Trions in Twisted Bilayer Graphene
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover
• Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
• Chern-insulator phases and spontaneous spin and valley order in a moiré lattice model for magic-angle twisted bilayer graphene
• The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
• Magnetic response of nematic superconductors: skyrmion stripes and their signatures in muon spin relaxation experiments
• Symmetries, Length Scales, Magnetic Response and Skyrmion Chains in Nematic Superconductors
• Unified picture of superconductivity and magnetism in CeRh${}_2$As${}_2$
• Intrinsic non-magnetic ${\varphi }_0$ Josephson junctions in twisted bilayer graphene
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• Theories for charge-driven nematicity in kagome metals
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Differential entropy per particle as a probe of van Hove singularities and flat bands
• Observation of near EF Fermi-arc van Hove singularity with prominent coupling to phonon in a van der Waals coupled Weyl semimetal