  Many-body calculations of the total energy of interacting Dirac electrons in
finite graphene samples exhibit joint occurrence of cusps at angular momenta
corresponding to fractional fillings characteristic of formation of
incompressible (gapped) correlated states (nu=1/3 in particular) and opening of
an insulating energy gap (that increases with the magnetic field) at the Dirac
point, in correspondence with experiments. Single-particle basis functions
obeying the zigzag boundary condition at the sample edge are employed in exact
diagonalization of the interelectron Coulomb interaction, showing, at all
sizes, mixed equal-weight bulk and edge components. The consequent depletion of
the bulk electron density attenuates the fractional-quantum-Hall-effect
excitation energies and the edge charge accumulation results in a gap in the
many-body spectrum.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons;Nuclear Theory;Atomic Physics