Magnetic Field Dependence of the Superconducting Penetration Depth in Thin Specimens

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Abstract
The magnetic field dependence of the superconducting penetration depth for very thin films as predicted by the Ginzburg-Landau theory is considered. The results obtained depend upon the boundary conditions on the film. For the usual case of equal magnetic fields on opposite sides of the film, the penetration depth increases smoothly toward infinity as the critical field is approached, corresponding to a second-order phase transition. For the less common case of unequal fields on opposite sides, the penetration depth increases toward a finite value as the critical field is approached, corresponding to a first-order phase transition. The results for the latter case are shown to agree remarkably well with the very precise experiments of Garwin, Erlbach, and Sarachik on the field dependence of the penetration depth of a 250 A film of Pb. The penetration depth in zero field as a function of thickness is also considered.