Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting transition temperature

Abstract

So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like (s- or d-wave) pairing theory is adequate for explaining high- $$T_\mathrm {c}$$ superconductivity in doped cuprates from underdoped to overdoped regime. We show that the doped cuprates, depending on the Fermi energy ( $$\varepsilon _\mathrm {F}$$ ) and the energy ( $$\varepsilon _\mathrm {A}$$ ) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $$\varepsilon _\mathrm {A}/\varepsilon _\mathrm {F}$$ and $$\Delta /\varepsilon _\mathrm {F}$$ (where $$\Delta $$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high- $$T_\mathrm {c}$$ superconductivity is quite different from the BCS-type (s- or d-wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ( $$T_\mathrm {c}$$ ) and the peculiar oxygen and copper isotope effects on $$T_\mathrm {c}$$ in overdoped cuprates.