Quasiparticle lifetime in disordered two-dimensional metals

A calculation of the electron quasiparticle lifetime in a disordered metal due to electron-electron scattering is given. The calculation takes account of the diffusive nature of electron motion which leads to enhancement of the diagonal exchange term of the electron self-energy. The lifetime, as a function of temperature, behaves as ${T}^{\ensuremath{-}\frac{d}{2}}$ where $d$ is the dimensionality, in contrast to the ${T}^{\ensuremath{-}2}$ behavior of ordinary Fermi-liquid theory. At $d=2$, a logarithmic singularity occurs which leads to ${(T\mathrm{ln}T)}^{\ensuremath{-}1}$ behavior of the lifetime and a failure of the quasiparticle picture near the Fermi surface. The calculated lifetime agrees in temperature, Fermi energy, and elastic mean-free-path dependence with recent experiments on silicon inversion layers.

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