Crossover from superfluidity to superconductivity in a system with doping dependent attraction

Zero temperature crossover from superfluidity to superconductivity with carrier density increasing is studied for a two-dimensional system in the s-wave and d-wave pairing channels. It was assumed that the particle attraction correlation length depends on carrier density nf as r0 ∼ 1/ √ nf . Such a dependence was found experimentally for the radius of magnetic correlations in La2−xSrxCuO4. The short range Coulomb repulsion was also taken into account. It is shown that the behavior of the system with doping is fundamentally different from the case with r0(nf ) = const. In particular, similarly to the d-wave case, the crossover in the s-channel takes place only if the coupling is larger of some minimal value, otherwise the Cooper pairing scenario takes place at any small carrier density. The relevance of the model to the high-temperature superconductors is discussed.