A Hartree-Fock study of the $\nu=0$ quantum Hall state of monolayer graphene with short range interactions

Abstract

Recent experiments involving tilted graphene samples have shown evidence of a continuous phase transition in the $\nu=0$ quantum Hall bulk state. We present here a simple model that supports such a transition. In addition to a long range SU(4) symmetric Coulomb interaction, we include Hubbard on-site and nearest neighbor interactions with tunable coupling strengths, and perform a self-consistent Hartree-Fock analysis. A large sea of negative energy Landau levels is retained, and is shown to have important qualitative and quantitative effects. Phase diagrams are constructed within the space of physically relevant parameters, yielding results consistent with experimental observation.