Spectral and optical properties of doped graphene with charged impurities in the self-consistent Born approximation

Spectral and transport properties of doped (or gated) graphene with long range charged impurities are discussed within the self-consistent Born approximation. It is shown how, for impurity concentrations greater than the electron concentration, $n_{imp} \geq n$, a finite DOS appears at the Dirac point, the one-particle lifetime no longer scales linearly with the Fermi momentum, and the lineshapes in the spectral function become non-lorentzian. These behaviors are different from the results calculated within the Born approximation. We also calculate the optical conductivity from the Kubo formula by using the self-consistently calculated spectral function in the presence of charged impurities.