The first Ginzburg-Landau equation for the order parameter ψ in the absence of magnetic fields is solved analytically for a superconducting slab of thickness 2d bordered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f=ψ/ψ∞ depends only on the transversal spatial coordinate x, normalized with respect to the coherence length ξ of the superconductor, provided the de Gennes boundary condition df/dx=f/b is used. The closed-form solution expresses x as an elliptic integral of f, depending on the normalized parameters d and b. It is predicted theoretically that, for b<∞ and d≤dc=arctan(1/b), the proximity effect is so strong that the superconductivity is completely suppressed. In fact, in this case, the first Ginzburg-Landau equation possesses only the trivial solution f≡0.
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Liniger, W. On the proximity effect in a superconductive slab bordered by metal. J Low Temp Phys 93, 1–6 (1993). https://doi.org/10.1007/BF00682277
- Boundary Condition
- Magnetic Field
- Wave Function
- Magnetic Material