Plasmons and Zeroth Sound in the Electron Gas

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Abstract
Zeroth sound waves are density oscillations in gases of fermions, interacting with short-range forces and undergoing infrequent scattering. Coulomb forces are long-ranged; in an electron gas, low-frequency (zeroth) sound waves are thereby replaced by high-frequency plasmons. Electron gases have charged particlelike excitations whose interactions are screened by the gas polarizability. It is therefore conceivable that density waves of such "quasiparticles" could arise having a typical sound spectrum. In most treatments, the quasiparticle interactions are phenomenological. We have studied this question with a single, nonphenomenological theory of sufficient complexity to show simultaneously both plasmons and the zeroth sound waves if they exist. We derive self-consistent-field equations which sound waves must satisfy, differing from those for plasmons only in the effective interactions; the Coulomb interactions are dynamically screened. The frequency dependence of the interactions makes self-consistency impossible. We conclude that the existence of zeroth sound in electron gases is unlikely.