On the Superconducting Critical Temperature of La\(_{2-x}\)Sr\(_{x}\)CuO\(_{4}\)/Sm\(_{2}\)CuO\(_4\) Superlattice: Polaronic Point of View of Stacking Periodicity Dependence

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.