Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
arXiv:2103.17270 · doi:10.1103/PhysRevB.103.205135
Abstract
Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively in these two systems chiral quasiparticles display linear and biquadratic band touching, leading to linearly vanishing and constant DOS. Consequently, the former system remains stable for weak enough local interactions, and supports a variety of ordered phases only beyond a critical strength of interactions. By contrast, ordered phases can nucleate for sufficiently weak interactions in bilayer graphene. By tuning the strength of all symmetry allowed local interactions, we construct various cuts of the phase diagram at zero and finite temperature and chemical doping. Typically, at zero doping insulating phases (such as charge-density-wave, antiferromagnet, quantum anomalous and spin Hall insulators) prevail at the lowest temperature, while gapless nematic or smectic liquids stabilize at higher temperatures. On the other hand, at finite doping the lowest temperature ordered phase is occupied by a superconductor. Besides anchoring such an organizing principle among the candidate ordered phases, we also establish a selection rule between them and the interaction channel responsible for the breakdown of linear or biquadrtic chiral nodal Fermi liquid. In addition, we also demonstrate the role of the normal state band structure in selecting the pattern of symmetry breaking from a soup of preselected incipient competing orders. As a direct consequence of the selection rule, while an antiferromagnetic phase develops in undoped monolayer and bilayer graphene, the linear (biquadratic) band dispersion favors condensation of a spin-singlet nematic (translational symmetry breaking Kekulé) superconductor in doped monolayer (bilayer) graphene, when the on site Hubbard repulsion dominates in these systems.
arXiv comment40 Pages, 13 Figures, 5 Tables (Published Version): extended abstract, see manuscript
References in corpus (106)
- The electronic properties of graphene
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Quantum Spin Hall Effect in Graphene
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Moire bands in twisted double-layer graphene
- Classification of topological quantum matter with symmetries
- Tuning superconductivity in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Graphene bilayer with a twist: electronic structure
- Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
- Dirac cones reshaped by interaction effects in suspended graphene
- Topological Semimetals
- Topological Mott Insulators
- Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
- Fermi-Hubbard physics with atoms in an optical lattice
- Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
- Interactions and phase transitions on graphene's honeycomb lattice
- Quantum Field Theory in the Large N Limit: a review
- Electron fractionalization in two-dimensional graphenelike structures
- Superconducting states of pure and doped graphene
- Marginal Fermi liquid behavior from 2d Coulomb interaction
- Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene
- Ghost excitonic insulator transition in layered graphite
- Is graphene in vacuum an insulator?
- Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
- Theory of interacting electrons on the honeycomb lattice
- Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
- Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
- Density waves and Cooper pairing on the honeycomb lattice
- Magnetic field-induced insulating behavior in highly oriented pyrolitic graphite
- Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
- Fermionic quantum criticality in honeycomb and -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
- Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
- Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
- Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
- Dynamical Screening and Ferroelectric-type Excitonic Instability in Bilayer Graphene
- Spontaneous symmetry breaking and Lifshitz transition in bilayer graphene
- Electron-electron interactions in graphene bilayers
- Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
- Spontaneously gapped ground state in suspended bilayer graphene
- Artificial graphene with tunable interactions
- Kohn-Luttinger superconductivity in graphene
- BCS superconductivity of Dirac electrons in graphene layers
- Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
- Interacting Weyl fermions: Phases, phase transitions and global phase diagram
- Multiple topological transitions in twisted bilayer graphene near the first magic angle
- Interacting fermions on the honeycomb bilayer: from weak to strong coupling
- Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
- Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
- Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
- Electronic multicriticality in bilayer graphene
- Weyl semimetals with short-range interactions
- Coulomb interaction at the metal-insulator critical point in graphene
- Phases of correlated spinless fermions on the honeycomb lattice
- Why does graphene behave as a weakly interacting system?
- Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
- Antiferromagnetism in the Hubbard Model on the Bernal-stacked Honeycomb Bilayer
- Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
- Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
- Transport Gap in Suspended Bilayer Graphene at Zero Magnetic Field
- Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
- Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
- Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
- Strain-induced time-reversal odd superconductivity in graphene
- Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
- Correlated spinless fermions on the honeycomb lattice revisited
- The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
- Phase diagram and Fermi-liquid properties of the extended Hubbard model on the honeycomb lattice
- Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
- Interaction-induced anomalous quantum Hall state on the honeycomb lattice
- Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly
- Multi-critical behavior of Gross-Neveu-Yukawa theory in graphene
- Stability of Dirac Liquids with Strong Coulomb Interaction
- Instabilities of Weyl-loop semi-metals
- Competing Ordered States in Bilayer Graphene
- Velocity renormalization and anomalous quasiparticle dispersion in extrinsic graphene
- Topological insulators in strained graphene at weak interaction
- Competing pairing channels in the doped honeycomb lattice Hubbard model
- Doping-induced quantum spin Hall insulator to superconductor transition
- Spin Symmetry of the Bilayer Graphene Groundstate
- Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
- Observation of topological Bloch-state defects and their merging transition
- Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities
- Superconductivity on the brink of spin-charge order in doped honeycomb bilayer
- Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
- Strongly Interacting Two-Dimensional Dirac Fermions
- Classification of massive and gapless phases in bilayer graphene
- Phase diagram of interacting spinless fermions on the honeycomb lattice
- Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
- Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram
- Superconducting and excitonic quantum phase transitions in doped systems with Dirac electrons
- Cooperon condensation and intra-valley pairing states in honeycomb Dirac systems
- Excitonic mass gap in uniaxially strained graphene
- Interaction-driven phases in a Dirac Semimetal: Exact Diagonalization Results
- Emergent chiral symmetry in a three-dimensional interacting Dirac liquid
- Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap
- Fermi-liquid ground state of interacting Dirac fermions in two dimensions
- Bond-ordered states and -wave pairing of spinless fermions on the honeycomb lattice
- Kekulé superconductivity and antiferromagnetism on the graphene lattice
- Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
- Explanation for the isotropy of the Dirac cone in graphene
- Novel criticality of Dirac fermions in the presence of emergent gauge fields
- Novel criticality of Dirac fermions from lattice symmetry breaking
- Coexistence of antiferromagnetism and topological superconductivity on the honeycomb lattice Hubbard model
- Mean-field quantum phase transition in graphene and in general gapless systems
- Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice
Cited by in corpus (29)
- Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene
- Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene
- Correlation-induced triplet pairing superconductivity in graphene-based moiré systems
- Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
- Quantum Electrodynamics of Non-Hermitian Dirac Fermions
- Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials
- Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
- From local spin nematicity to altermagnets: Footprints of band topology
- Nodal pair density waves from a quarter-metal in crystalline graphene multilayers
- Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
- Superconducting phase transition in planar fermionic models with Dirac cone tilting
- Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the -wave superconductors
- Non-unitary multiorbital superconductivity from competing interactions in Dirac materials
- Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
- Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry
- Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
- Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
- Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
- Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
- Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
- Superconductivity in doped planar Dirac insulators: A renormalization group study
- Fault-tolerant quantum simulation of generalized Hubbard models
- Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
- Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
- Superconductivity in three-dimensional interacting doped topological insulators
- Ordered states in AB bilayer graphene in SU(4)-symmetric model
- Pair density wave in quarter metals from a repulsive fermionic interaction in graphene heterostructures: A renormalization group study
- Charge density waves and stripes in quarter metals of graphene heterostructures
- Phase diagram of the SU Fermi-Hubbard model with next-neighbor interactions