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

We describe a variational theory for incompressible ground states and charge gaps in the N = 0 Landau level of graphene that accounts for the fourfold Landau level degeneracy and the short-range interactions that break SU(4) spin-valley invariance. Our approach explains the experimental finding that gaps at odd numerators are weak for 1 < vertical bar nu vertical bar < 2 and strong for 0 < vertical bar nu vertical bar < 1. We find that in the SU(4) invariant case the incompressible ground state at vertical bar nu vertical bar = 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.