Charge-density waves in two- and three-dimensional jellium

The stability of the electron gas in jellium against the formation of charge-density waves is studied using the density-functional formalism. Charge-density waves occur in three-dimensional jellium for $r_s>26\mathrm{}$ and in two dimensions for $r_s>17\mathrm{}$ in our approximation. The theory is applied to two-dimensional electron gases on liquid-helium surfaces and in semiconductors.