Proximity effect in zero field with the Landau-Ginzburg equation. I

The proximity effect can be explained by solving the complete Landau-Ginzburg equation. The solution of the equation naturally produces a simple and explicit expression of the transition temperature for a film sandwich composed of a bulk superconductor and a normal metal. The gene- ral result obtained is ${\mathit{T}}_{\mathit{c}\mathit{S}\mathit{N}}$/${\mathit{T}}_{\mathit{c}\mathit{S}}$=t=1-${\mathit{B}}_0$ ${\mathit{d}}_{\mathit{N}}$ ${\xi }_{\mathit{S}}$/(${\mathit{d}}_{\mathit{S}}^2$+3d ${}_{\mathit{N}}{}^{}{}_{}{}^{}$ ${\mathit{d}}_{\mathit{S}}$/k) or an alternative, t=[1-${\mathit{B}}_0$ ${\mathit{d}}_{\mathit{N}}$ ${\xi }_{\mathit{S}}$/(${\mathit{d}}_{\mathit{S}}^2$+3${\mathit{d}}_{\mathit{N}}$ ${\mathit{d}}_{\mathit{S}}$/k)${]}^{1/2}$. The theoretical calculations fit experimental results very well.