Plasmon dispersion in strongly correlated superlattices

The dielectric response function of a strongly correlated superlattice is calculated in the quasilocalized charge (QLC) approximation. The resulting QLC static local-field correction, which contains both intralayer and interlayer pair-correlational effects, is identical to the correlational part of the third-frequency-moment sum-rule coefficient. This approximation treats the interlayer and intralayer couplings on an equal footing. The resulting dispersion relation is first analyzed to determine the effect of intralayer coupling on the out-of-phase acoustic-mode dispersion; in this approximation the interlayer coupling is suppressed and the mutual interaction of the layers is taken into account only through the average random-phase approximation (RPA) field. In the resulting mode dispersion, the onset of a finite-k (k being the in-plane wave number) reentrant low-frequency excitation developing (with decreasing d/a) into a dynamical instability is indicated (a being the in-plane Wigner-Seitz radius and d the distance between adjacent lattice planes). This dynamical instability parallels a static structural instability reported earlier both for a bilayer electron system and a superlattice and presumably indicates a structural change in the electron liquid. If one takes account of interlayer correlations beyond the RPA, the acoustic excitation spectrum is dramatically modified by the appearance of an energy gap which also has a stabilizing effect on the instability. We extend a previous energy gap study at k=0 [G. Kalman, Y. Ren, and K. I. Golden, Phys Rev. B 50, 2031 (1994)] to a calculation of the dispersion of the gapped acoustic excitation spectrum in the long-wavelength domain.