Electron correlations in quantum and classical plasmas in a layered structure

We present a theoretical calculation of electron correlations in quantum and classical plasmas in a layered structure. This treatment rests on the solution of the first member of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and the fluctuation-dissipation theorem. For arbitrary wave number this leads to a set of coupled integral equations which has to be solved self-consistently. In the long-wavelength limit it is found that the phase velocity of the collective excitation is renormalized due to short-range correlations. Our result is an extension of the earlier theory of K. S. Singwi et al. [Phys. Rev. 176, 589 (1968)] for bulk plasmas to the case of a layered electron gas. Our numerical results show that the correlation function for a layered structure is an oscillatory function of the lattice period, which reflects the interference between the density fluctuations in different layers.