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.

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

References in corpus (22)

• Electronic States of Graphene Nanoribbons
• Unconventional Integer Quantum Hall effect 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
• The zero-energy state in graphene in a high magnetic field
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• 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
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• 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
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Electronic properties of graphene and graphene nanoribbons with "pseudo-Rashba" spin-orbit coupling
• 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
• Noncollinear magnetic phases and edge states in graphene quantum Hall bars
• Diffusion on edges of insulating graphene with intravalley and intervalley scattering

Cited by in corpus (3)

• Absence of edge reconstruction for quantum Hall edge channels in graphene devices
• 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