Edge and Surface States in the Quantum Hall Effect in Graphene

Abstract

We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge states (generated by the magnetic field) and Anderson-localized surface states (created by the presence of zig-zag edges) lead to edge reconstruction. As a consequence, the point contact tunneling on a graphene edge has a non-universal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of $e^2/h$. We argue that the magneto-transport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.

9 pages, 6 figures. This is the final and extended version of our manuscript that was published in Physical Review B. It contains a detailed discussion on the effects of disorder on the surface and edge states in graphene

References in corpus (18)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Electronic Properties of Disordered Two-Dimensional Carbon
• Unconventional Integer Quantum Hall effect in graphene
• One-Dimensional Fermi liquids
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene
• Unconventional quasiparticle lifetime in graphite
• Reentrant Metallic Behavior of Graphite in the Quantum Limit
• Zero-Conductance Resonances due to Flux States in Nanographite Ribbon Junctions
• Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet
• Reconstruction of Fractional Quantum Hall Edges
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• Coulomb drag by small momentum transfer between quantum wires
• Fermi liquid to Luttinger liquid transition at the edge of a two-dimensional electron gas
• Current drag in capacitevly coupled Luttinger constrictions
• Coulomb Drag between Quantum Wires
• Electron-phonon interactions on a single-branch quantum Hall edge

Cited by in corpus (83)

• The electronic properties of graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Properties of Graphene: A Theoretical Perspective
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Weak localisation magnetoresistance and valley symmetry in graphene
• Magneto-optical conductivity in Graphene
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Graphene: new bridge between condensed matter physics and quantum electrodynamics
• Electron transport in disordered graphene
• Intrinsic Half-Metallicity in Modified Graphene Nanoribbons
• Optical and magneto-optical far-infrared properties of bilayer graphene
• The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene
• Observation of Landau levels of Dirac fermions in graphite
• Conductance quantization in mesoscopic graphene
• Quantum dots in graphene
• Quantum conductance of graphene nanoribbons with edge defects
• Coulomb blockade in graphene nanoribbons
• Novel electric field effects on Landau levels in Graphene
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Perfectly Conducting Channel and Universality Crossover in Disordered Nano-Graphene Ribbons
• Optical conductivity of bilayer graphene with and without an asymmetry gap
• Nonlinear screening of charge impurities in graphene
• Low energy theory of disordered graphene
• Thermo-Plasma Polariton within Scaling Theory of Single-Layer Graphene
• Luttinger Liquid at the Edge of a Graphene Vacuum
• Electron-Electron Interactions on the Edge States of Graphene: A Many Body Configuration Interaction Study
• Proximity Induced Superconductivity and Multiple Andreev Reflections in Few-Layer-Graphene
• Transport in disordered graphene nanoribbons
• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• Edge phonons in black phosphorus
• Pomeranchuk and Topological Fermi Surface Instabilities from Central Interactions
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Electron waves in chemically substituted graphene
• Möbius Graphene Strip as Topological Insulator
• Robust zero-averaged wave-number gap inside gapped graphene superlattices
• Topological Insulating States in Laterally Patterned Ordinary Semiconductors
• Weak Localization of Dirac Fermions in Graphene
• Thermo-Electric Power of Dirac Fermions in Graphene
• Nearly Perfect Single-Channel Conduction in Disordered Armchair Nanoribbons
• Interplay between lattice-scale physics and the quantum Hall effect in graphene
• Lattice-Induced Double-Valley Degeneracy Lifting in Magnetic Field in Graphene
• A real-space study of random extended defects in solids : application to disordered Stone-Wales defects in graphene
• Sensory Organ like Response of Zigzag Edge Graphene Nanoribbons
• Correlated Electronic Properties of Some Graphene Nanoribbons: A DMRG Study
• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
• Plateau insulator transition in graphene
• Valley polarization effects on the localization in graphene Landau levels
• States near Dirac points of rectangular graphene dot in a magnetic field
• Terahertz Transverse-Electric- and Transverse-Magnetic-polarized waves localized on graphene in photonic crystals
• Electronic properties of a graphene antidot in magnetic fields
• Hall Coefficient of Dirac Fermions in Graphene under Charged Impurity Scatterings
• Quantum Hall effect in ac driven graphene: from half-integer to integer case
• Nernst effect of Dirac fermions in graphene under weak magnetic field
• Magnetic Field Effects on the Superconducting and Quantum Critical Properties of Layered Systems with Dirac Electrons
• Topological Surface States in Paramagnetic and Antiferromagnetic Iron Pnictides
• Phase diagrams and edge-state transitions in graphene with spin-orbit coupling and magnetic and pseudomagnetic fields
• Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator
• Landau level transitions indoped graphene in a time dependent magnetic field
• Magnetoconductivity of Dirac fermions in graphene under charged impurity scatterings
• Valley-kink in Bilayer Graphene at $\nu =0$: A Charge Density Signature for Quantum Hall Ferromagnetism
• Quenching of the quantum Hall effect in graphene with scrolled edges
• Edge States at the Interface between Monolayer and Bilayer Graphene
• Dirac equation in low dimensions: The factorization method
• Robustness of persistent currents in two-dimensional Dirac systems with disorders
• Relativistic fermion on a ring: Energy spectrum and persistent current
• Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
• Gap opening in the zeroth Landau level in gapped graphene: Pseudo-Zeeman splitting in an angular magnetic field
• Transport properties of hybrid single-bilayer graphene interfaces in magnetic field
• Persistent current of relativistic electrons on a Dirac ring in presence of impurities
• Charge and spin Hall effect in graphene with magnetic impurities
• Differential Conductance Fluctuation of Curved Nanographite Sheets in the Mesoscopic Regime
• Absence of edge states at armchair edges in inhomogeneously strained graphene under a pseudomagnetic field
• Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid
• Accurate densities of states for disordered systems from free probability: Live Free or Diagonalize
• Edge states in a honeycomb lattice: effects of anisotropic hopping and mixed edges
• Transverse transport in graphite
• Increased metallicity of Carbon nanotubes because of incorporation of extended Stone-Wales' defects: an ab-initio real space approach
• Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes
• Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene
• The Universal Edge Physics in Fractional Quantum Hall Liquids
• Effects of a Magnetic Field on Superconductivity and Quantum Criticality in Quasi-Two-Dimensional Systems with Dirac Electrons
• Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction