Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions

Abstract

We study possible patterns for spontaneous symmetry breaking in a Dirac fermion model, which is applicable to twisted bilayer graphene at charge neutrality. We show how a chiral SU(4) symmetry emerges and construct the corresponding low-energy model that includes a Fierz-complete set of symmetry-allowed four-fermion interactions. We employ an unbiased renormalization group treatment to identify the critical points that describe transitions into different ordered phases. The resulting phase diagram depends on the number of fermion flavours and we show that the coupling between ordering channels prevents many of the possible mean-field orders from being accessible at relevant, small flavour numbers. We argue that, as a consequence, twisted bilayer graphene is governed by a quantum Hall state or an SU(4) manifold of insulating spin-valley orders with emergent Lorentz symmetry that contains inter-valley coherent, spin Hall, and valley Hall states. We study how SU(4)-breaking perturbations affect the accessibility and can additionally stabilize symmetry-broken (semi-)metallic states.

arXiv commentFInal version accepted in PRB, 11+9 pages, 5+5 figures

References in corpus (89)

• 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
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Graphene bilayer with a twist: electronic structure
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Dirac materials
• Aspects of the Functional Renormalisation Group
• Origin of Magic Angles in Twisted Bilayer Graphene
• Functional renormalization group approach to correlated fermion systems
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• The nonperturbative functional renormalization group and its applications
• Moiré heterostructures as a condensed matter quantum simulator
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Untying the insulating and superconducting orders in magic-angle graphene
• Electronic structure of turbostratic graphene
• Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Mapping the twist angle and unconventional Landau levels in magic angle graphene
• Phonon scattering dominated electron transport in twisted bilayer graphene
• Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Renormalization group analysis of the 2D Hubbard model
• Theory of interacting electrons on the honeycomb lattice
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
• Flavour Hund's Coupling, Correlated Chern Gaps, and Diffusivity in Moiré Flat Bands
• Entropic evidence for a Pomeranchuk effect in magic angle graphene
• Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
• Symmetry broken Chern insulators and magic series of Rashba-like Landau level crossings in magic angle bilayer graphene
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene
• Quantum Hall Effect, Screening and Layer-Polarized Insulating States in Twisted Bilayer Graphene
• Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Strain-induced quantum phase transitions in magic angle graphene
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Magnetism, superconductivity, and spontaneous orbital order in iron-based superconductors: who comes first and why?
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Bootstrapping 3D Fermions with Global Symmetries
• Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
• Global Phase Diagram of the Normal State of Twisted Bilayer Graphene
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Critical behavior of Dirac fermions from perturbative renormalization
• UV fixed-point structure of the three-dimensional Thirring model
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking
• Chiral Symmetry Breaking in Graphene
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Renormalization group study of interaction-driven quantum anomalous Hall and quantum spin Hall phases in quadratic band crossing systems
• Ising and Gross-Neveu model in next-to-leading order
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Strain-induced time-reversal odd superconductivity in graphene
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene
• Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Fermion-induced quantum criticality with two length scales in Dirac systems
• 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
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Nodal band-off-diagonal superconductivity in twisted graphene superlattices
• Mott multicriticality of Dirac electrons in graphene
• Quantum phase transitions in Dirac fermion systems
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Nematic insulator at charge neutrality in twisted bilayer graphene
• Critical exponent $\eta$ at $O(1/N^3)$ in the chiral XY model using the large $N$ conformal bootstrap
• Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential

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