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Marginal Fermi Liquid from a Partially Nested Fermi Surface and Impurity Scattering in a Two Dimensional Metal

The electron-electron scattering rate of low-energy quasiparticles is computed perturbatively for a two-dimensional metal with a partially nested Fermi surface, a weak electron-electron interaction and an energy-independent impurity scattering rate. We show that even when the nested section comprises only a small fraction of the Fermi surface, the low energy quasiparticle decay rates throughout the Fermi surface gain a term which is linear in energy $ω$. The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate $δ$. We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.