Dynamic gap generation in graphene under the long-range Coulomb interaction

Dynamic gap generation in graphene under the long-range Coulomb interaction is studied by the Dyson-Schwinger gap equation beyond the instantaneous approximation. Once the dependence of the dynamic gap on the energy has been considered, the critical interaction strength alpha(c) decreases to 0.542. If the renormalization of the fermion velocity is considered, alpha(c) will become alpha(c) = 1.02. This indicates that the dependence on the energy and the renormalization of the fermion velocity are both important for dynamic gap generation in graphene under long-range Coulomb interaction.