Theory of Anomalous Quantum Hall Effects in Graphene

Abstract

Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. One of the most remarkable properties of graphene is the anomalous quantum Hall effect. It is extremely sensitive to the structure of the system; in particular, it clearly distinguishes single- and double-layer samples. In spite of the impressive experimental progress, the theory of quantum Hall effect in graphene has not been established. This theory is a subject of the present paper. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. The Hall quantization is due to Anderson localization which, in graphene, is very peculiar and depends strongly on the character of disorder. It is only a special symmetry of disorder that may give rise to anomalous quantum Hall effects in graphene. We analyze the symmetries of disordered single- and double-layer graphene in magnetic field and identify the conditions for anomalous Hall quantization.

13 pages (article + supplementary material), 5 figures

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• Ballistic transport in disordered graphene
• The nature of localization in graphene under quantum Hall conditions
• Transversal magnetoresistance in Weyl semimetals
• Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene
• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Transition to Landau Levels in Graphene Quantum Dots
• Quantum Hall plateau transition in graphene with spatially correlated random hopping
• Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices
• Dissipation and criticality in the lowest Landau level of graphene
• Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
• Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Quantum Hall effect in bilayer and multilayer graphenes with finite gate voltage
• Quantum chaos in disordered graphene
• Interaction and disorder effects in 3D topological insulator thin films
• Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point
• Strong magnetoresistance of disordered graphene
• Quantum magnetooscillations in the ac conductivity of disordered graphene
• Disorder-driven splitting of the conductance peak at the Dirac point in graphene
• Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
• Conductance fluctuations and disorder induced $\nu =0$ quantum Hall plateau in topological insulator nanowires
• Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties
• Splitting of critical energies in the $n$=0 Landau level of graphene
• Generalization of Chiral Symmetry for Tilted Dirac Cones
• High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian
• Lattice realization of the generalized chiral symmetry in two dimensions
• Topologically protected Landau levels in bilayer graphene in finite electric fields
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Narrow depression in the density of states at the Dirac point in disordered graphene
• Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders
• Magnetic-field driven ambipolar quantum Hall effect in epitaxial graphene close to the charge neutrality point
• Gap opening in the zeroth Landau level in gapped graphene: Pseudo-Zeeman splitting in an angular magnetic field
• Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion
• Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level
• Orbital magnetic moments in insulating Dirac systems: Impact on magnetotransport in graphene van der Waals heterostructures
• Engineering metal-$s{p}_{xy}$ Dirac bands on the oxidized SiC surface
• Composite Fermion Nonlinear Sigma Models
• Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regime
• Relevant perturbations at the spin quantum Hall transition
• Conduction properties of extended defect states in Dirac materials
• Shape of the zeroth Landau level in graphene with non-diagonal disorder
• Quantized heat flow in graphene quantum Hall phases: Probing the topological order
• Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
• Spectroscopic signatures of different symmetries of the superconducting order parameter in metal-decorated graphene