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Phase structure of monolayer graphene is studied on the basis of a U(1) gaugetheory defined on the honeycomb lattice. Motivated by the strong couplingexpansion of U(1) lattice gauge theory, we consider on-site andnearest-neighbor interactions between the fermions. When the on-siteinteraction is dominant, the sublattice symmetry breaking (SLSB) of thehoneycomb lattice takes place. On the other hand, when the interaction betweennearest neighboring sites is relatively strong, there appears two differenttypes of spontaneous Kekule distortion (KD1 and KD2), without breaking thesublattice symmetry. The phase diagram and phase boundaries separating SLSB,KD1 and KD2 are obtained from the mean-field free energy of the effectivefermion model. A finite gap in the spectrum of the electrons can be induced inany of the three phases.

Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice