Dynamical gap generation in graphene with frequency dependent renormalization effects

We study the frequency dependencies in the renormalization of the fermion Greens function for the $\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.