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

TL;DR

This paper simplifies the analysis of edge excitations in the canted antiferromagnetic phase of the $ u=0$ quantum Hall state in graphene, revealing how the edge gap closes with increasing parallel magnetic field, leading to an insulator-metal transition.

Contribution

It provides a mean-field calculation of edge excitation spectra in the CAF phase, showing how the edge gap varies with magnetic field orientation and identifying a transition to a metallic phase.

Findings

Edge gap decreases with increasing parallel magnetic field.

The edge gap closes at a critical field, indicating a transition to a metallic phase.

Conductance increases exponentially with the parallel magnetic field in the CAF phase.

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 $B_\parallel^*$ 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 $0<B_\parallel<B_\parallel^*$, 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 $\nu=0$ quantum Hall state in a tilted-field experiment.