Wave-vector-dependent plasmon linewidth in the alkali metals

Abstract

The nearly-free-electron (NFE) pseudopotential theory is used to calculate the wave-vector-dependent plasmon linewidth due to interband transitions in lithium, sodium, and potassium. It is shown that interband excitations constitute the dominant decay mechanism which for all alkali metals results in a decreasing linewidth for small $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$, contrary to a recent model calculation by Gibbons. Together with estimates of contributions from two particlehole pair excitations and from phonon- and impurity-assisted intraband and interband transitions, the resulting linewidth is compared with experiment. In Li, the total linewidth decreases for $k\ensuremath{\lesssim}0.5{k}_{F}$, as borne out by experiment, whereas for Na and K the contribution from pair-pair excitations leads finally to an increasing linewidth, in qualitative agreement with experiment. Remaining quantitative discrepancies suggest that interband transitions to empty $d$ bands beyond the NFE model contribute to the plasmon linewidth in K and possibly also in Na.