Superconducting Condensate Formation in Metallic Systems with Arbitrary Carrier Density (review)

This article gives a contemporary and to some extent pedagogical review of the current theoretical understanding of the formation of the superconducting state in metallic systems with a variable density of carriers. We make an attempt to describe the crossover from the Bose-Einstein condensation type (small densities) to the Bardeen-Cooper-Schrieffer one (large densities). The functional methods are used throughout the treatment. The most of the results are considered in a review form for the first time. Some of them (in particular, the possible opening of a pseudogap) are used to explain the experimental data avaliable for high-temperatures superconductors.