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

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