Electron self-energy effects on chiral symmetry breaking in graphene

Abstract

We investigate the dynamical breakdown of the chiral symmetry in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for the dynamical gap generation in the ladder approximation, showing that it blows up at a critical value α c in the graphene fine structure constant, which is quite sensitive to many-body corrections. Under static random phase approximation (RPA) screening of the interaction potential, we find that taking into account electron self-energy corrections to the vertex increases the critical coupling to α c 4.9, for a number N=4 of two-component Dirac fermions. When dynamical screening of the interaction is instead considered, the effect of Fermi velocity renormalization in the electron and hole states leads to the value α c1.75 for N=4, substantially larger than that obtained without electron self-energy corrections (-0.99), but still below the nominal value of the interaction coupling in isolated free-standing graphene. © 2012 American Physical Society.