Thickness dependence of the superconducting transition temperature of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>−</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>films

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.

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