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 nonperturbative Dyson-Schwinger approach. Compared to the results of our previous calculation [M. E. Carrington et al., Phys. Rev. B 94, 125102 (2016)], which used a Lindhard screening approximation instead of including a self-consistently calculated dynamical screening function, the critical coupling is substantially reduced.