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

Abstract

We perform a simplified analysis of the edge excitations of the canted antiferromagnetic (CAF) phase of the $\nu =0$ 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 ${\Delta }_{\text{edge}}$ 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 (${\Delta }_{\text{edge}}=0$) once the F phase, characterized by gapless counter-propagating edge excitations, is reached at some finite $B_{\perp }$-dependent value $B_{\parallel }^{\ast }$ and remains closed upon further increase of $B_{\parallel }$. This results in an gradual insulator-metal transition, in which the conductance $G\sim (e^2/h)\exp (-{\Delta }_{\text{edge}}/T)$ grows exponentially with $B_{\parallel }$ in the range $0<B_{\parallel }<B_{\parallel }^{\ast }$, while in the gapped CAF phase, and saturates to a metallic value $G\sim e^2/h$ in the F phase at $B_{\parallel }>B_{\parallel }^{\ast }$. This unique transport feature of the CAF phase provides a way to identify and distinguish it from other competing phases of the $\nu =0$ quantum Hall state in a tilted-field experiment.

11 pages, 6 figs

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