ν=0 Quantum Hall state in a finite graphene sheet and at finite temperature

The quantum Hall state at ν=0 in graphene arises due to electronic interactions, giving rise to ordered states via the mechanism of magnetic catalysis. We consider the situation in which the ordered state is a canted antiferromagnet (AFM), supporting easy-plane AFM accompanied by an easy-axis ferromagnetic moment. Accounting for both strong Landau level mixing and finite size effects, we demonstrate that the canted-AFM undergoes a continuous quantum phase transition to a ferromagnetic state in the presence of a strong tilted magnetic field. We use parameters (such as interaction strengths) consistent with measurements of the bulk gap in a perpendicular magnetic field to study the edge states and establish a semi-quantitative agreement with recent experimental observations of such transition. In addition, we also include the effects of thermal fluctuations for the order parameters in the canted-AFM phase and proprose scalings for the transition temperature of the quantum Hall ordered phases at fillings ν=0 and ν=1, which can directly be verified in experiments.