Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps

Abstract

By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for the interpretation of recent experiments are discussed.

arXiv comment13 pages, 7 figures. v2: analysis for ribbons with armchair edges added, to appear in Phys. Rev. B

References in corpus (51)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Electronic Properties of Disordered Two-Dimensional Carbon
• Electronic States of Graphene Nanoribbons
• Unconventional Integer Quantum Hall effect in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Graphene: new bridge between condensed matter physics and quantum electrodynamics
• Interactions and phase transitions on graphene's honeycomb lattice
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Magnetic field driven metal-insulator phase transition in planar systems
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene
• Ghost excitonic insulator transition in layered graphite
• The zero-energy state in graphene in a high magnetic field
• Theory of interacting electrons on the honeycomb lattice
• Edge States and the Quantized Hall Effect in Graphene
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Magnetic field-induced insulating behavior in highly oriented pyrolitic graphite
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• 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
• Dirac Fermion Confinement in Graphene
• Theory of integer quantum Hall effect in graphene
• Symmetry of boundary conditions of the Dirac equation for electrons in carbon nanotubes
• Competition between spin and charge polarized states in nanographene ribbons with zigzag edges
• Spontaneous parity breaking of graphene in the quantum Hall regime
• Excitonic instability in two-dimensional degenerate semimetals
• Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field
• Hidden multiferroic order in graphene zigzag ribbons
• Luttinger Liquid at the Edge of a Graphene Vacuum
• Collapse of Spin-Splitting in the Quantum Hall Effect
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Charge and Spin Transport at the Quantum Hall Edge of Graphene
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Intrinsic Zeeman Effect in Graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Dissipation and criticality in the lowest Landau level of graphene
• Toward theory of quantum Hall effect in graphene
• Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band
• Fractal structure of the effective action in (quasi-) planar models with long-range interactions
• Quantum Hall plateau transition in the lowest Landau level of disordered graphene

Cited by in corpus (23)

• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Gate-Defined Graphene Quantum Point Contact in the Quantum Hall Regime
• Exploring the graphene edges with coherent electron focusing
• Electronic states of pseudospin-1 fermions in dice lattice ribbons
• Surface Magnetic Catalysis
• Localized electron states near the armchair edge of graphene
• States near Dirac points of rectangular graphene dot in a magnetic field
• Edge magnetoplasmons in graphene
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Formation mechanism of bound states in graphene point contacts
• To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons
• Absence of Perfect Conductance Quantization of Helical-edge Transport in Graphene under a Strong, Tilted Magnetic Field
• Dirac Kondo effect under magnetic catalysis
• Edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential: finite frequency gaps and zero group velocity
• Propagation of acoustic edge waves in graphene under quantum Hall effect
• Zigzag edge states in graphene in the presence of in-plane electric field
• Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields
• Edge states in bilayer graphene in a magnetic field
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Rotation Symmetry Spontaneous Breaking of Edge States in Zigzag Carbon Nanotubes