On the proximity effect in a superconductive slab bordered by metal

Abstract

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≤d_c=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.