HARTREE-FOCK STUDIES OF QUANTUM HALL STATES IN GRAPHENE

Abstract

Recent experiments involving tilted graphene samples in the quantum Hall regime have shown strong evidence of a continuous phase transition in the v = 0 bulk state. The origins of this transition are rooted in SU(4) symmetry-breaking interactions. In this work, we present a model with microscopic interactions that supports such a transition. The model is studied within a self-consistent Hartree-Fock analysis. We find that the full set of possible symmetry-breaking terms in the interactions are realized by incorporating an active window of non-zero Landau levels in the Hartree-Fock state. Additionally, the model is studied away from integer filling, in which Skyrme crystals supporting spin textures are stabilized by long range Coulomb interactions. We explore how these textures evolve with the system parameters, and construct a phase diagram within the space of the Zeeman strength and filling factor.