Specific criteria for determining the fermionic and bosonic natures of Cooper pairs in doped cuprate superconductors

Abstract We argue that the underlying mechanism of superconductivity in condensed matter system depends on the fermionic or bosonic nature of superfluid charge carriers and examine the possibility of the existence of bosonic (polaronic) Cooper pairs and fermionic (conventional) Cooper pairs in doped copper oxides (cuprates) accordingly at intermediate and high doping levels. We show that the superfluid Cooper pairs in doped cuprates depending on the doping level (or Fermi energy ε F ) and the characteristic energy ξ A of the attractive interaction between pairing charge carriers (i.e. polarons and quasi-free holes) might be either weakly-bound (overlapping) fermionic Cooper pairs or tightly-bound (non-overlapping) bosonic Cooper pairs. We obtain the specific quantitative criteria for determining the fermionic and bosonic natures of Cooper pairs and the possibility of the existence of such Cooper pairs in two different Bardeen-Cooper-Schrieffer (BCS) - type and Bose-type cuprate superconductors, depending on the two fundamental ratios ξ A /ε F and ∆ F /ε F (where ∆ F is the BCS-like energy gap in the excitation spectra of cuprate superconductors). We identify the key and distinctive behaviors of Cooper pairs in underdoped, optimally doped and overdoped cuprate superconductors. We demonstrate that the polaronic Cooper pairs in underdoped and optimally doped cuprates exhibit bosonic behavior and these high- T c materials with small Fermi energies ε F ≃ (0.1 ÷ 0.2) eV are in the limit of unconventional (Bose-type) superconductors, but Cooper pairs of quasi-free holes in overdoped cuprates with relatively large Fermi energies ε F > 0.3 eV exhibit fermionic behavior and such doped cuprate materials are in the limit of conventional BCS-type superconductors just like usual metals.