Lifetime of a quasiparticle in a two-dimensional electron gas

Abstract

We have investigated the inelastic Coulomb lifetime ${\tau }_{\mathrm{ee}}$ of a quasiparticle near to the Fermi surface of a two-dimensional electron gas. Within a perturbative approach based upon the random-phase approximation, we find that at low temperature $\frac{1}{{\tau }_{\mathrm{ee}}}$ behaves like $T^2\ln T$. Furthermore at small quasiparticle excitation energy, the leading contribution to $\frac{1}{{\tau }_{\mathrm{ee}}}$ is inversely proportional to the electronic density and does not depend upon the electric charge. Although the plasmon frequency goes to zero at long wavelength, plasmon emission contributes to the quasiparticle decay only when the quasiparticle excitation energy exceeds a certain threshold. The threshold becomes a small fraction of the Fermi energy in the high-density limit.