Edge Reconstruction in Monolayer Graphene at and near ν=0

Monolayer graphene in a magnetic field at ν=0 theoretically displays a variety of phases,
such as the canted antiferromagnet, the fully polarized, the charge density wave, and Kekule
distorted, depending on the external and internal couplings[1]. In this problem we focus on the
edge of a graphene sheet when the confining potential is made smoother. An analysis at
ν=3 in GaAs quantum Hall systems shows a novel spin-mode- switching, where the
spatial order of the spin modes switches to make like-spin edges lie close to each other[2].
We will study the similarities and differences between the Dirac-like quantum Hall system of
monolayer graphene and standard GaAs systems and show that pseudospin-mode- switching
occurs in graphene edges near ν=0.

[1] Maxim Kharitonov, Phys. Rev. B 85, 155439
[2] Udit Khanna, Ganpathy Murthy, Sumathi Rao, and Yuval Gefen, Phys. Rev. Lett. 119, 186804