Many-body effects in graphene beyond the Dirac model with Coulomb interaction

This paper is devoted to the development of perturbation theory for studying the properties of graphene sheets of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and arbitrary interaction potential between electrons, which is considered as a perturbation. One-loop corrections to the electron propagator and to the interaction potential at nonzero temperature and chemical potential are calculated. One-loop formulas for the energy spectrum of electrons in graphene, for the renormalized Fermi velocity and also for the dielectric permittivity, are derived.