Abstract
We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors ν_G=-2+n/3 (n=2,4,5). We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully SU(4) symmetric limit. For all the fractions we study there are two-component states for which the competing phases are generalizations of those occurring at neutrality ν_G=0. They are ferromagnetic, antiferromagnetic, charge-density wave and K\'ekul\'e phases, depending on the values of Ising or XY anisotropies in valley space. The varying spin-valley content of the states leads to ground state quantum numbers that are different from the ν_G=0 case. For filling factor ν_G=-2+5/3 there is a parent state in the SU(4) limit which has a flavor content (1,1/3,1/3,0) where the two components that are one-third filled form a two-component singlet. The addition of anisotropies leads to the formation of new states that have no counterpart at ν_G=0. While some of them are predicted by the variational approach, we find notably that negative Ising-like valley anisotropy leads to the formation of a state which is a singlet in both spin and valley space and lies beyond the reach of the variational method. Also fully spin polarized two-component states at ν=-2+4/3 and ν=-2+5/3 display an emergent SU(2) valley symmetry because they do not feel point-contact anisotropies. We discuss implications for current experiments concerning possible spin transitions.