Evolution from BCS superconductivity to Bose condensation: Role of the parameterkFξ

We argue that the natural variable to establish the crossover from Cooper-pair-based superconductivity to Bose-Einstein condensation of bound-electron pairs is the product ${\mathit{k}}_{\mathit{F}}$ξ of Fermi electron wave vector times the coherence length for two-electron correlation, and that Cooper-pair-based superconductivity is stable against bosonization down to ${\mathit{k}}_{\mathit{F}}$ξ≃2π. We also propose that the experimental plot by Uemura et al., relating the superconducting temperature ${\mathit{T}}_{\mathit{c}}$ to the Fermi temperature ${\mathit{T}}_{\mathit{F}}$ for a variety of ‘‘exotic’’ as well as conventional superconductors, can be rationalized by correlating the ratio ${\mathit{T}}_{\mathit{c}}$/${\mathit{T}}_{\mathit{F}}$ to ${\mathit{k}}_{\mathit{F}}$ξ. It appears in this way that the high-${\mathit{T}}_{\mathit{c}}$ superconductors lie in the plot by Uemura et al. near the ‘‘instability’’ line ${\mathit{k}}_{\mathit{F}}$ξ=2π.