Angular dependence of the critical magnetic field in granular superconducting films

Abstract

The critical magnetic fieldH _c (ϑ) of granular Al films has been measured as a function of the angle ϑ between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length ξ(T), the “bulk” electron mean free path1 is smaller than the BCS coherence length ξ₀, and 1$\begin{gathered} \gtrsim \hfill \\< \hfill \\ \end{gathered}$ d. The experimental data onH _c (ϑ) are well fitted by the Tinkham formula. However, the observed values ofH _c∥/H _c⊥are not always consistent with${{2\sqrt 3 \xi (T)} \mathord{\left/ {\vphantom {{2\sqrt 3 \xi (T)} d}} \right. \kern-\nulldelimiterspace} d}$ and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c (ϑ) and that the enhancement ofH _c∥is larger than that ofH _c⊥.