Intermediate type-I superconductors in the mesoscopic scale

M. Tinkham [Introduction to Superconductivity, 2nd ed. (Dover, Mineola, NY, 2004), Chap. 4, pp. 135-138] and P. G. de Gennes [Superconductivity of Metals and Alloys (Benjamin, New York, 1966), Chap. 6, pp. 199-201] described the existence of an intermediate type-I superconductor as a consequence of an external surface that affects the well-known classification of superconductors into type I and II. Here we consider the mesoscopic superconductor where the volume-to-area ratio is small and the effects of the external surface are enhanced. By means of the standard Ginzburg-Landau theory, the Tinkham-de Gennes scenario is extended to the mesoscopic type-I superconductor. We find additional features of the transition at the passage from the genuine to the intermediate type I. The latter has two distinct transitions, namely from a paramagnetic to diamagnetic response in descending field, and a quasi-type-II behavior as the critical coupling 1/2 is approached in ascending field. The intermediate type-I phase proposed here, and its corresponding transitions, reflect intrinsic features of the superconductor and not its geometrical properties.