Many-body interaction effects in doped and undoped graphene: Fermi liquid versus non-Fermi liquid

Abstract

We consider theoretically the electron-electron interaction induced many-body effects in undoped (``intrinsic'') and doped (``extrinsic'') two-dimensional (2D) graphene layers. We find that (1) intrinsic graphene is a marginal Fermi liquid with the imaginary part of the self-energy, $\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})$, varying linearly in energy $\ensuremath{\omega}$ for small $\ensuremath{\omega}$, implying that the quasiparticle spectral weight vanishes at the Dirac point as ${(\mathrm{ln}\phantom{\rule{0.2em}{0ex}}\ensuremath{\omega})}^{\ensuremath{-}1}$; and (2) extrinsic graphene is a well-defined Fermi liquid with $\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}\ensuremath{\omega}$ near the Fermi surface similar to 2D carrier systems with parabolic energy dispersion. We provide analytical and numerical results for quasiparticle renormalization in graphene, concluding that all experimental graphene systems are ordinary 2D Fermi liquids since any doping automatically induces generic Fermi liquid behavior.