Instability of layered quantum liquids: 4. Intraplane and interplane correlations

We calculate the local-field correctionsG(q, q_z) f electron superlattices with interlayer distanced in order to describe many-body effects. A generalized Hubbard expression for the local-field correction is derived. The sum-rule version of the self-consistent approach for the local-field correction is developed and used to discuss the effects of exchange and correlation. The RPA-parameterr_s and the ratiod/a^* determine the many-body effects.a^* is the effective Bohr radius. The stability region for the Fermi liquid behavior of the layered electron gas is discussed: (i) forda^* the critical RPA-parameterr_sc1 is determined by exchange andintraplane correlation effects, (ii) forda^* withr_sc1 correlation effects are small and the instability point is mainly determined by exchange effects, (iii) forda^* withr_sc<1 exchange andinterplane correlation effects are both important for the instability point. Our results are important for high-T_c superconductors, organic superconductors and semiconductor superlattices.