Thickness dependence of the superconducting transition temperature ofLa2−xSrxCuO4films

A model of the strain effect on the transition temperature $T_c$ of superconducting films is presented. Details are given for previously published results on the thickness dependence of $T_c$ in the (001) ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$ films. A key role is played by the strain resulting from lattice mismatch between the film and the substrate, which is responsible for the behavior of $T_c.$ Calculations show that the values of $T_c$ of the films on ${\mathrm{SrLaAlO}}_4$ substrates under compressive strain are always higher than those on ${\mathrm{SrTiO}}_3$ under tensile strain. As the thickness is reduced, the films grown on ${\mathrm{SrTiO}}_3$ substrates exhibit a rapid reduction of $T_c,$ whereas the $T_c$ increases on ${\mathrm{SrLaAlO}}_4$ substrates. The theoretical results are in good agreement with experiments.