Superconducting Films in Perpendicular Fields and the Effect of the de Gennes Parameter

In this paper we study superconductivity of a thin film placed in a perpendicular magnetic field. We discuss the dependence of the upper critical field HC3 on the thickness l of the film and the Ginzburg--Landau parameter $\kappa$, and we examine nucleation of superconductivity. We show that a critical change occurs at $l=2\gamma\kappa^{-2}$. If $l>a\kappa^{-2}$ ($a>2\gamma$), the film exhibits type II behaviors: as the applied magnetic field decreases from $H_{C_3}$, superconductivity nucleates in a strip at the lateral surface and develops a lateral surface superconducting state. If $l\leq 2\g\kappa^{-2}+C\kappa^{-4}$, the film exhibits type I behaviors.

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