Quasiparticle properties of a simple metal at high electron temperatures

We compute the real and imaginary parts of the quasiparticle self-energy $\Sigma$ due to the electron-electron interaction for electrons and holes in jellium and crystalline Al at electron temperatures approaching the Fermi temperature $T_{\mathrm{F}}.$ $\mathrm{Re}\Sigma$ and $\mathrm{Im}\Sigma$ are computed using a finite temperature generalization of the $\mathrm{GW}$ approximation. We find a decrease in the electron lifetime and an increase in the valence and conduction bandwidths as T is increased. Calculation of the spectral function $A(k,E)\mathrm{}$ reveals that the total weight in the quasiparticle peak is a very weak function of T, and that the basic peak structure remains for $T\sim \mathrm{few}\times {0.1T}_{\mathrm{F}}.$ These predictions suggest that at these electron temperatures, the prominent peak in the absorption spectrum of Al at $\sim 1.5\hspace{0.5em}\mathrm{eV}$ should be washed out due to lifetime broadening, even if the ions remain in their crystalline positions.