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We calculate the single-particle spectral function for doped bilayer graphenein the low energy limit, described by two parabolic bands with zero band gapand long range Coulomb interaction. Calculations are done using thermal Green'sfunctions in both the random phase approximation (RPA) and the fullyself-consistent GW approximation. RPA (in line with previous studies) yields aspectral function which apart from the Landau quasiparticle peaks showsadditional coherent features interpreted as plasmarons, i.e. compositeelectron-plasmon excitations. In GW the plasmaron becomes incoherent and peaksare replaced by much broader features. The deviation of the quasiparticleweight and mass renormalization from their non-interacting values is smallwhich indicates that bilayer graphene is a weakly interacting system. Theelectron energy loss function, $Im[-\epsilon^{-1}_q(\omega)]$ shows a sharpplasmon mode in RPA which in GW approximation becomes less coherent and thusconsistent with the weaker plasmaron features in the correspondingsingle-particle spectral function.

Bilayer graphene spectral function in RPA and self-consistent GW