This paper investigates the superconductivity of La \(_{2-x}\) Sr \(_{x}\) CuO \(_{4}\) /Sm \(_{2}\) CuO \(_4\) superlattices using a theoretical approach based on the extended Holstein model and bipolaronic mechanism for high-temperature superconductivity. We analyzed the dependence of the superconducting critical temperature ( \(T_c\) ) on the thickness of the La \(_{1.85}\) Sr \(_{0.15}\) CuO \(_4\) layer ( \(d_f\) ) within the superlattice, which can also be expressed as the number of La \(_{1.85}\) Sr \(_{0.15}\) CuO \(_4\) half-unit cells ( \(N_{stc.p}\) ). Our model assumes that the charge carriers in superconducting La \(_{1.85}\) Sr \(_{0.15}\) CuO \(_4\) layers are bipolarons. We associate high-temperature superconductivity with the superfluidity of the liquid of intersite bipolarons and estimate the superfluidity transition temperature as the Bose-Einstein condensation temperature ( \(T_{BEC}\) ) of the gas (liquid) of intersite bipolarons. In this way, we directly link the superlattice’s \(T_c\) with the corresponding Bose-Einstein condensation temperature ( \(T_{BEC}\) ). Numerical calculations revealed a strong correlation between \(T_c\) and \(T_{BEC}\) . Importantly, these calculations accurately reproduce the experimental trend of \(T_c\) with respect to \(d_f\) or \(N_{stc.p}\) . Our results strongly suggest that strain-induced polaronic effects play a critical role in the superconductivity of La \(_{2-x}\) Sr \(_{x}\) CuO \(_{4}\) /Sm \(_{2}\) CuO \(_4\) superlattices, further supporting the validity of the bipolaronic model for high-temperature superconductivity in cuprates.
