INSTABILITY OF LAYERED QUANTUM LIQUIDS .1. LOCAL-FIELD CORRECTION IN SUPERLATTICES

For a superlattice with period d the Singwi et al. (Phys. Rev. 176, 589 (1968)) approach for the local-field correction and the static structure factor is formulated. With two approximations we reduce the resulting three-dimensional integral-equation into a one-dimensional integral-equation. For the local-field correction we present analytical results for small wave numbers and large wave numbers. An expression of Hubbard-typ is derived for the local-field correction. Explicit results for boson superlattices and electron superlattice are given. A charge-density-wave instability in a layered Bose condensate with r(s) > r(sc) is-proportional-to d3/4 is discovered. r(s) is the small parameter of the random-phase-approximation. The charge-density-wave instability is due to a many-body anomaly (short-range correlations) in layered structures and is a general property of layered quantum liquids. We find the charge-density-wave instability in a layered electron gas for r(s) > r(sc) is-proportional-to d. Double-quantum-well structures are also considered. The effects of a finite well width is calculated. The general implications of the charge-density-wave instability for microscopically layered quantum liquids are pointed out.