Abstract
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) ford≫a * the critical RPA-parameterr sc≫1 is determined by exchange andintraplane correlation effects, (ii) ford≈a * withr sc≈1 correlation effects are small and the instability point is mainly determined by exchange effects, (iii) ford≪a * 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.
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