Edge states, mass and spin gaps, and quantum Hall effect in graphene

Abstract

Motivated by recent experiments and a theoretical analysis of the gap equation for the propagator of Dirac quasiparticles, we assume that the physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field is connected with the generation of both Dirac masses and spin gaps. The consequences of such a scenario for the existence of the gapless edge states with zigzag and armchair boundary conditions are discussed. In the case of graphene on a half-plane with a zigzag edge, there are gapless edge states in the spectrum only when the spin gap dominates over the mass gap. In the case of an armchair edge, however, the existence of the gapless edge states depends on the specific type of mass gaps.

14 pages, 7 figures

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Cited by in corpus (35)

• Properties of Graphene: A Theoretical Perspective
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• Canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in bilayer graphene
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene
• WKB analysis of edge states in graphene in a strong magnetic field
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Transconductance fluctuations as a probe for interaction induced quantum Hall states in graphene
• Unique nature of the lowest Landau level in finite graphene samples with zigzag edges: Dirac electrons with mixed bulk-edge character
• Collective Edge Modes near the onset of a graphene quantum spin Hall state
• Theory of integer quantum Hall effect in insulating bilayer graphene
• Electron-hole coexistence in disordered graphene probed by high-field magneto-transport
• Stability of edge states in strained graphene
• Collective Bulk and Edge Modes through the Quantum Phase Transition in Graphene at $\nu =0$
• Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Interacting electrons in graphene nanoribbons in the lowest Landau level
• Edge magnetotransport in graphene: A combined analytical and numerical study
• A Hartree-Fock study of the $\nu =0$ quantum Hall state of monolayer graphene with short range interactions
• Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene
• Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene
• Diffusion on edges of insulating graphene with intravalley and intervalley scattering
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Absence of Perfect Conductance Quantization of Helical-edge Transport in Graphene under a Strong, Tilted Magnetic Field
• Featuring nuanced electronic band structure in gapped multilayer graphene
• 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
• Edge states in bilayer graphene in a magnetic field
• 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
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• On topological aspects of 2D graphene like materials