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^-d/2 where d is the dimensionality, in contrast to the T^-2 behavior of ordinary Fermi-liquid theory. At $d=2$, a logarithmic singularity occurs which leads to (TlnT)^-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.