Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems

Abstract

In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J=1 and J=2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including assessing the role of disorder in current experimental results. Special attention is given to the interesting low magnetic field limit and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.

References in corpus (40)

• The electronic properties of graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Room-Temperature Quantum Hall Effect in Graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Unconventional Integer Quantum Hall effect in graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Electronic states and Landau levels in graphene stacks
• Multicomponent fractional quantum Hall effect in graphene
• The zero-energy state in graphene in a high magnetic field
• Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
• Edge States and the Quantized Hall Effect in Graphene
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Pseudospin Magnetism in Graphene
• Quantum Anomalous Hall State in Bilayer Graphene
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Theory of integer quantum Hall effect in graphene
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Lattice Theory of Pseudospin Ferromagnetism in Bilayer Graphene: Competing Orders and Interaction Induced Quantum Hall States
• Fractional Quantum Hall Effect in Graphene
• Intra-Landau level Cyclotron Resonance in Bilayer Graphene
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• Order from Disorder in Graphene Quantum Hall Ferromagnet
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• Intrinsic Zeeman Effect in Graphene
• Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at $\nu =0$ in High Magnetic Fields
• Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene
• Charge 2e skyrmions in bilayer graphene
• Non-Fermi Liquid behavior in Neutral Bilayer Graphene
• Atypical Fractional Quantum Hall Effect in Graphene at Filling Factor 1/3
• Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect
• Testing the topological nature of the fractional quantum Hall edge
• The enigma of the nu=0 quantum Hall effect in graphene
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

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• Fractional topological phases and broken time reversal symmetry in strained graphene
• Generalized effective hamiltonian for graphene under non-uniform strain
• Selective equilibration of spin and valley polarized quantum Hall edge states in graphene
• Superconducting States in pseudo-Landau Levels of Strained Graphene
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Weak-field Hall Resistivity and Spin/Valley Flavor Symmetry Breaking in Magic-Angle Twisted Bilayer Graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Theory of unconventional quantum Hall effect in strained graphene
• Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors -- A Perspective Review
• Spin Superfluidity in the $\nu =0$ Quantum Hall State of Graphene
• Acoustic Wave Absorption as a Probe of Dynamical Geometrical Response of Fractional Quantum Hall Liquids
• Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening
• Quantum Hall ferromagnetic phases in the Landau level N=0 of a graphene bilayer
• Landau level splittings, phase transitions, and non-uniform charge distribution in trilayer graphene
• Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization
• Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system
• Coulomb impurity under magnetic field in graphene: a semiclassical approach
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• Classification of massive and gapless phases in bilayer graphene
• Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene
• Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene
• Local two-body parent Hamiltonians for the entire Jain sequence
• Higher vortexability: zero field realization of higher Landau levels
• Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference
• Robust helical edge transport at $\nu =0$ quantum Hall state
• Quantum Hall Valley Nematics
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Topological superconductivity in Quantum Hall-superconductor hybrid systems
• A Holographic Quantum Hall Ferromagnet
• Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
• Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene
• Voltage Scaling of Graphene Device on SrTiO3 Epitaxial Thin Film
• Landau level transitions indoped graphene in a time dependent magnetic field
• Gap generation in ABC-stacked multilayer graphene: screening vs band flattening
• Topological Aspects of Fermions on Hyperdiamond
• Weak Coupling Theory of Magic-Angle Twisted Bilayer Graphene
• Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
• Order-from-disorder and critical scalings of spontaneous magnetization in random-field quantum spin systems
• Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Validity of the two-band model of bilayer and trilayer graphene in a magnetic field
• Boosting energy levels in graphene magnetic quantum dots through magnetic flux and inhomogeneous gap
• Edge spin excitations and reconstructions of integer quantum Hall liquids
• Magnetic Phases in Periodically Rippled Graphene
• Inducing a metal-insulator transition in disordered interacting Dirac fermion systems via an external magnetic field
• Holographic D3-probe-D5 Model of a Double Layer Dirac Semimetal
• The Ground State of Monolayer Graphene in a Strong Magnetic Field
• Transport gap and hysteretic behavior of the Ising quantum Hall ferromagnets in Landau levels $\left|N\right|>0$ of bilayer graphene
• Electron trapping in graphene quantum dots with magnetic flux
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene
• Ising quantum Hall ferromagnetism in Landau levels $\left|N\right|\ge 1$ of bilayer graphene
• Electromagnetic absorption and Kerr effect in quantum Hall ferromagnetic states of bilayer graphene
• Hofstadter-Moiré Butterfly in Twisted Trilayer Graphene
• Exciton crystal melting and destruction by disorder in bilayer quantum hall system with total filling factor one
• Competing topological phases in few-layer graphene
• Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field
• Electron with arbitrary pseudo spins in multilayer graphene
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Semiclassical perspective on Landau levels and Hall conductivity in an anisotropic Cubic Dirac Semi-Metal and the peculiar case of star-shaped classical orbits