Chiral Symmetry and Electron-Electron Interaction in Many-Body Gap Formation in Graphene

We study a many-body ground state of graphene in perpendicular magnetic fields. Chiral symmetry in graphene enables us to determine the many-body ground state, which turns out to be a doubly degenerate chiral condensate for the half-filled (undoped) case. In the ground state a prominent charge accumulation emerges along zigzag edges. We also show that gapless excitations are absent despite the presence of the robust edge modes, which is consistent with the Chern number C = 0.