Evolution from BCS superconductivity to Bose condensation: Role of the parameter kFξ

Abstract

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 kFξ 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 kFξ≃2π. We also propose that the experimental plot by Uemura et al., relating the superconducting temperature Tc to the Fermi temperature TF for a variety of ‘‘exotic’’ as well as conventional superconductors, can be rationalized by correlating the ratio Tc/TF to kFξ. It appears in this way that the high-Tc superconductors lie in the plot by Uemura et al. near the ‘‘instability’’ line kFξ=2π.

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