Dynamical Mass Generation of Composite Dirac Fermions and Fractional Quantum Hall Effects near Charge Neutrality in Graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to dynamical mass generation through exciton condensation. The four-fold spin-valley degeneracy is fully lifted due to the mass generation and the exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of the composite Dirac fermions. At the filling factor $\nu=1/2$, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired nonabelian state described by the Moore-Read Pfaffian in the long wavelength limit.