Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene

Abstract

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu =0$ and $\nu =\pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|\nu |=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu =0$ and $|\nu |=1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.

arXiv comment5 pages, 3 figures + Supplementary Materials (3.5 pages, 2 figures): Published version, typos corrected, new references

References in corpus (48)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Boron nitride substrates for high-quality graphene electronics
• Unconventional Integer Quantum Hall effect in graphene
• Electronic Properties of Graphene in a Strong Magnetic Field
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Strength of effective Coulomb interactions in graphene and graphite
• Interactions and phase transitions on graphene's honeycomb lattice
• Multicomponent fractional quantum Hall effect in graphene
• Magnetic field driven metal-insulator phase transition in planar systems
• Spin and valley quantum Hall ferromagnetism in graphene
• Ghost excitonic insulator transition in layered graphite
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Interaction phenomena in graphene seen through quantum capacitance
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Lattice field theory simulations of graphene
• Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Theory of integer quantum Hall effect in graphene
• Spontaneous parity breaking of graphene in the quantum Hall regime
• Interaction driven instabilities of a Dirac semi-metal
• Excitonic instability in two-dimensional degenerate semimetals
• Fractional Quantum Hall Phase Transitions and Four-flux Composite Fermions in Graphene
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Why does graphene behave as a weakly interacting system?
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• Topological Fermi liquids from Coulomb interactions in the doped Honeycomb lattice
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Composite Dirac fermions in graphene
• Quantum critical scaling in magnetic field near the Dirac point in graphene
• Integer and Fractional Quantum Hall Effect in Two-Terminal Measurements on Suspended Graphene
• Theory of integer quantum Hall effect in insulating bilayer graphene
• Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction

Cited by in corpus (44)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Composite Fermions and Broken Symmetries in Graphene
• Magnetic catalysis and axionic charge-density-wave in Weyl semimetals
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• STM Study of Quantum Hall Isospin Ferromagnetic States of Zero Landau Level in Graphene Monolayer
• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Edge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Spin Superfluidity in the $\nu =0$ Quantum Hall State of Graphene
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Edge structure of graphene monolayers in the ν = 0 quantum Hall state
• Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators
• Magnetic Catalysis in Graphene Effective Field Theory
• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Collective Bulk and Edge Modes through the Quantum Phase Transition in Graphene at $\nu =0$
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Emergence of helical edge conduction in graphene at the ν=0 quantum Hall state
• A Hartree-Fock study of the $\nu =0$ quantum Hall state of monolayer graphene with short range interactions
• Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime
• Ferromagnetism and glassiness on the surface of topological insulators
• Coulomb interactions, Dirac sea polarization and $SU(4)$ symmetry breaking of the integer quantum Hall states of graphene
• Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
• SO(8) Fermion Dynamical Symmetry and Strongly-Correlated Quantum Hall States in Monolayer Graphene
• The Ground State of Monolayer Graphene in a Strong Magnetic Field
• Magnetic catalysis in weakly interacting hyperbolic Dirac materials
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Absence of Perfect Conductance Quantization of Helical-edge Transport in Graphene under a Strong, Tilted Magnetic Field
• Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene
• Integer Quantum Hall Effect of Interacting Electrons in Graphene
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Dirac Kondo effect under magnetic catalysis
• Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields
• Orbital magnetization of interacting Dirac fermions in graphene
• SU(4) symmetry breaking revealed by magneto-optical spectroscopy in epitaxial graphene
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Fractional Quantum Hall Filling Factors from String Theory using Toric Geometry
• Uniquely identifying quantum Hall phases in charge neutral graphene