The phenomenon of exciton-fermion condensation

Conditions are investigated under which a finite density of excitons can arise spontaneously, which then mediate BCS-type pairing of free electrons through virtual excitonic transitions involving higher state (excited) excitonic levels. This cooperative exciton-fermion condensation, which takes place primarily via a first-order phase transition that is close to second order, is characterized by large values of the ratio of the superconducting gap to the transition temperature, even when the coupling constant is small. In the limit of small free-electron densities and high temperatures, polaron effects give rise to a discontinuity in the exciton concentration, leading to a considerable relaxation of the conditions for subsequent appearance of the superconducting condensate. It is shown that the maximum transition temperatures for a given position of the Fermi level correspond to a line of critical points. Near this critical line, the nature of the exciton transition turns out to be irrelevant, which eliminates any direct or indirect influence of the isotopic shift on the transition temperature. The applicability of the model to layered superconducting oxides is discussed