Broken SU(4) Symmetry and The Fractional Quantum Hall Effect in Graphene

We construct a variational description for incompressible ground states and charge gaps in the N = 0 LL of graphene which accounts for the 4-fold Landau level degeneracy and for the short range interactions that break the SU(4) spin-valley invariance. Our approach explains the experimental finding that gaps at odd numerators are weak for 1<|\nu|<2 and strong for 0<|\nu|< 1. We find that in the SU(4) invariant case the incompressible ground state at |\nu|=1/3 is a three-component incompressible state, not the Laughlin state, and discuss the competition between these two states in the presence of SU(4) spin-valley symmetry breaking terms.