Texture Transitions of Quantum Hall Skryme Crystals Near Charge Neutrality in Graphene

How does the quantum Hall canted antiferromagnetic (CAF) groundstate of graphene transition into the ferromagnet when the system is doped away from zero filling factor? We study this question within a self-consistent Hartree-Fock theory, in which regular Skyrme crystals are stabilized by long range Coulomb interactions. In addition to this we include a Hubbard on-site term in the Hamiltonian which breaks the symmetry in the valley degree of freedom, and stabilizes a CAF state when the Zeeman energy is not too large. The full set of possible symmetry-breaking terms in the interactions are realized by incorporating an active window of non-zero Landau levels in our Hartree-Fock state. We explore how textures in the various discrete degrees of freedom evolve with the system parameters, and discuss the consequences of this for the phase diagram within the space of the on-site Hubbard parameter, Zeeman strength, and filling factor.