Dynamical gap generation in graphene with frequency-dependent renormalization effects

We study the frequency dependencies in the renormalization of the fermion Green's 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.

Figure 1

The fermion Dyson-Schwinger equation in Eq. (8) with self-energy given in Eq. (9) and photon propagator in (15, 16, 17, 18, 19). The blobbed line and vertex represent, respectively, the dressed fermion propagator and the dressed vertex.

Figure 2

Momentum dependence of the $Z$ and $A$ dressing functions.

Figure 3

Momentum dependence of the $\mathrm{\Delta }$ dressing function.

Figure 4

$\widehat{\mathrm{\Delta }}$ versus $\alpha$. The extrapolated values of the critical coupling are given in Table 1.

Figure 5

The renormalized Fermi velocity.