Mesoscopic samples: the superconducting condensate via the Gross-Pitaevskii scenario

Mesoscopic superconductors are routinely investigated with the Ginzburg-Landau equations, whereby the confinement is taken into account by imposing that the normal component of the superconducting current vanishes through the sample boundary. We argue that this approach gives misleading results when applied to micron- and submicron-sized devices, and we introduce modified Ginzburg-Landau equations that take the confinement potential into account on the level of the free energy functional. For devices much larger than the Ginzburg-Landau coherence length, both approaches agree, but deviations appear for samples of the scale of the coherence length. In the absence of a magnetic field, the modified Ginzburg-Landau equation for the order parameter reduces to the Gross-Pitaevskii equation.