ON THE PROXIMITY EFFECT IN A SUPERCONDUCTIVE SLAB BORDERED BY METAL

The first Ginzburg-Landau equation for the order parameter psi in the absence of magnetic fields is solved analytically for a superconducting stab of thickness 2d bordered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f = psi/psi(infinity) depends only on the transversal spatial coordinate x, normalized with respect to the coherence length xi 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 < infinity and d less-than-or-equal-to 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.