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Using many-body diagrammatic perturbation theory we consider carrier density-and substrate-dependent many-body renormalization of doped or gated grapheneinduced by Coulombic electron-electron interaction effects. We quantitativelycalculate the many-body spectral function, the renormalized quasiparticleenergy dispersion, and the renormalized graphene velocity using theleading-order self-energy in the dynamically screened Coulomb interactionwithin the ring diagram approximation. We predict experimentally detectablemany-body signatures, which are enhanced as the carrier density and thesubstrate dielectric constant are reduced, finding an intriguing instability inthe graphene excitation spectrum at low wave vectors where interactioncompletely destroys all particle-like features of the noninteracting lineardispersion. We also make experimentally relevant quantitative predictions aboutthe carrier density and wave-vector dependence of graphene velocityrenormalization induced by electron-electron interaction. We compare on-shelland off-shell self-energy approximations within the ring diagram approximation,finding a substantial quantitative difference between their predicted velocityrenormalization corrections in spite of the generally weak-coupling nature ofinteraction in graphene.

Velocity renormalization and anomalous quasiparticle dispersion in extrinsic graphene