Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene

Abstract

Edge excitations of the $\nu =0$ quantum Hall state in monolayer graphene are studied within the mean-field theory with different symmetry-breaking terms. The analytical expressions for the continuum (Dirac) model wave functions are obtained for the charge density wave, Kekulé distortion, ferromagnetic, and (canted) antiferromagnetic phases. The dispersion equations for each phase and boundary type (zigzag and armchair) are derived, numerically solved, and compared to the results of the corresponding effective tight-binding model. The effect of the next-to-nearest neighbor hopping parameter on the edge state spectrum is studied and revealed to be essential. The criteria for the existence of gapless edge states are established for each phase and edge type.

arXiv comment14 pages, 5 figures, published version: minor changes, references and Fig.4 added

References in corpus (51)

• 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
• Electronic Properties of Disordered Two-Dimensional Carbon
• Electronic States of Graphene Nanoribbons
• Unconventional Integer Quantum Hall effect in graphene
• Observation of the Fractional Quantum Hall Effect in Graphene
• Electronic Properties of Graphene in a Strong Magnetic Field
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Quantum-limited shot noise in graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene
• The zero-energy state in graphene in a high magnetic field
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Electronic properties of graphene antidot lattices
• Theory of integer quantum Hall effect in graphene
• Stabilization mechanism of edge states in graphene
• Symmetry of boundary conditions of the Dirac equation for electrons in carbon nanotubes
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene
• Luttinger Liquid at the Edge of a Graphene Vacuum
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Accurate determination of electron-hole asymmetry and next-nearest neighbor hopping in graphene
• Magnetoresistance measurements of Graphene at the Charge Neutrality Point
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Valley-isospin dependence of the quantum Hall effect in a graphene p-n junction
• Antiferromagnetic state in bilayer graphene
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Deconfined fractional electric charges in graphene at high magnetic fields
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
• Electronic properties of graphene and graphene nanoribbons with "pseudo-Rashba" spin-orbit coupling
• Half-integer contributions to the quantum Hall conductivity from single Dirac cones
• Dirac boundary condition at the reconstructed zigzag edge of graphene
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening
• Landau levels, edge states, and strained magnetic waveguides in graphene monolayers with enhanced spin-orbit interaction
• Noncollinear magnetic phases and edge states in graphene quantum Hall bars
• The quantum Hall effect in graphene - a theoretical perspective
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene
• Diffusion on edges of insulating graphene with intravalley and intervalley scattering
• Edge states in bilayer graphene in a magnetic field

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• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Microwave Imaging of Edge Conductivity in Graphene at Charge Neutrality and Quantum Hall States