A minimal size for granular superconductors

We investigate the minimal size of small superconducting grains by means of a Ginzburg-Landau model confined to a sphere of radius R. This model is supposed to describe a material in the form of a ball, whose transition temperature when presented in bulk form, T₀, is known. We obtain an equation for the critical temperature as a function of R and of T₀, allowing us to obtain a minimal radius of the sphere below which no superconducting transition exists. An estimate of values of minimal radii for different materials is done.