Unusual isotope effects on the pseudogap in high-Tc cuprate superconductors as support for the BCS-like pairing theory of large polarons above Tc

The BCS-like pairing theory is extended to the intermediate coupling regime and to the cases of exotic cuprate superconductors with large and small Fermi surfaces, so as to describe the pairing correlations above Tc, the opening of a pseudogap (PG) at a mean-field temperature T∗>Tc and the unusual isotope effects on the PG in these materials within the large polaron model and two different BCS-like approaches. We argue that unconventional electron-phonon interactions are responsible for the polaron formation and the separation between temperatures T∗ (the onset of precursor Cooper pairing) and Tc (the onset of the superconducting transition) in exotic cuprate superconductors. Using the extended BCS-like approaches, we calculate the PG formation temperature T∗, isotope shifts ΔT∗, oxygen and copper isotope exponents and show that isotope effects on the PG basically depend on strengths of Coulomb and electron-phonon interactions, doping levels and dielectric constants of the cuprates. The new BCS-like pairing theory of polaronic carriers predicts the existence of small and sizable positive oxygen isotope effect and very large negative oxygen and copper isotope effects on the PG in the cuprates with large Fermi surfaces. The calculated results for T∗, isotope shifts and exponents are compared with experimental data on various cuprate superconductors. For all the considered cases, a good quantitative agreement was found between theory and experimental data. We also predict the existence of small and sizable negative isotope effects on T∗ in deeply underdoped cuprates with small Fermi surfaces. Further, we find that the isotope effects on T∗(=Tc) in heavily overdoped cuprates just like in some metals are relatively small positive or become even negative.