Interacting electrons in graphene studied under the renormalized ring diagram approximation

Using the tight-binding model with long-range Coulomb interactions between electrons, we study some of the electronic properties of graphene. The Coulomb interactions are treated with the renormalized ring diagram approximation. By self-consistently solving the integral equations for the Green's function, we calculate the spectral density. The obtained result is in agreement with experimental observation. In addition, we also compute the density of states, the distribution functions, and the ground-state energy. Within the present approximation, we find that the imaginary part of the self-energy fixed at the Fermi momentum varies as quadratic in energy close to the chemical potential and then shows a linear dependence at larger energies within a certain range, regardless of whether the system is doped or not. This result appears to indicate that the electrons in graphene always behave like a moderately correlated Fermi liquid.