The role of frequency dependence in dynamical gap generation in graphene

We study the frequency dependencies of the fermion and photon dressing functions in dynamical gap generation in graphene. We use a low energy effective QED-like description, but within this approximation, we include all frequency dependent effects including retardation. We obtain the critical coupling by calculating the gap using a non-perturbative Dyson-Schwinger approach. Compared to the results of our previous calculation [1] which used a Lindhard screening approximation instead of including a self-consistently calculated dynamical screening function, the critical coupling is substantially reduced.