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Edge excitations of the canted antiferromagnetic phase of the $ν=0$ quantum Hall state in graphene: a simplified analysis

We perform a simplified analysis of the edge excitations of the canted antiferromagnetic (CAF) phase of the $ν=0$ quantum Hall state in both monolayer and bilayer graphene. Namely, we calculate, within the framework of quantum Hall ferromagnetism, the mean-field quasiparticle spectrum of the CAF phase neglecting the modification of the order parameter at the edge. We demonstrate that, at a fixed perpendicular component $B_\perp$ of the magnetic field, the gap $Δ_\text{edge}$ in the edge excitation spectrum gradually decreases upon increasing the parallel component $B_\parallel$, as the CAF phase continuously transforms to the fully spin-polarized ferromagnetic (F) phase. The edge gap closes completely ($Δ_\text{edge}=0$) once the F phase, characterized by gapless counter-propagating edge excitations, is reached at some finite $B_\perp$-dependent value $B_\parallel^*$ and remains closed upon further increase of $B_\parallel$. This results in an gradual insulator-metal transition, in which the conductance $G \sim (e^2/h) \exp(-Δ_\text{edge}/T)$ grows exponentially with $B_\parallel$ in the range $0<B_\parallel<B_\parallel^*$, while in the gapped CAF phase, and saturates to a metallic value $G \sim e^2/h$ in the F phase at $B_\parallel>B_\parallel^*$. This unique transport feature of the CAF phase provides a way to identify and distinguish it from other competing phases of the $ν=0$ quantum Hall state in a tilted-field experiment.