Abstract
The dielectric function ε(q, ω), for arbitrary wave vector q and frequency ω, is calculated in the random phase approximation (RPA), for the cases of (i) a single layer and (ii) a pair of layers of two-dimensional electron gas where the electrons in the different layers are interacting with by the coulomb force but no electronic transfer does occur between the different layers. Closed expressions for the plasmon dispersion relation are derived for both cases. For the single layer case, it is shown that the widely believed \sqrtq type plasmon dispersion relation stands for only in a very narrow region near q=0 which becomes narrower as the carrier density increases. For the case of a pair of layers, two plasmon branches are obtained; in the long wavelength limit, one has a \sqrtq type dispersion relation and the other has a linear dispersion relation in q, that is, an acoustic plasmon. The calculations are extended to the system of N layers and the condition for the appearance of an acoustic plasmon branch is discussed.
