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We investigate the dynamical breakdown of the chiral symmetry in the theoryof Dirac fermions in graphene with long-range Coulomb interaction. We analyzethe electron-hole vertex relevant for the dynamical gap generation in theladder approximation, showing that it blows up at a critical value \alpha_c inthe graphene fine structure constant which is quite sensitive to many-bodycorrections. Under static RPA screening of the interaction potential, we findthat taking into account electron self-energy corrections to the vertexincreases the critical coupling to \alpha_c \approx 4.9, for a number N = 4 oftwo-component Dirac fermions. When dynamical screening of the interaction isinstead considered, the effect of Fermi velocity renormalization in theelectron and hole states leads to the value \alpha_c \approx 1.75 for N = 4,substantially larger than that obtained without electron self-energycorrections (\approx 0.99), but still below the nominal value of theinteraction coupling in isolated free-standing graphene.

Electron self-energy effects on chiral symmetry breaking in graphene