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 $1<|\nu |<2$ 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.

• Received 24 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.126804