Superconducting properties in granular aluminum films near percolation threshold

We have measured the perpendicular upper critical magnetic field H-C2, the excess conductance sigma ' due to superconducting fluctuations and the supe rconducting transition temperature Te in granular aluminum films in the wid e range of the sheet resistance R-square, 100 Omega less than or equal to R -square less than or equal to 15 k Omega. The temperature dependence of H-C 2 near T-C has been analyzed in the form H-C2 = H-C2(0)(1 - T/T-C)(n). For relatively low resistance films, the index n is almost unit. However, n dec reases steeply at a characteristic resistance R degrees approximate to 1.5 k Omega and approaches 0.7 with increase of R-square. This value of n agree s with that predicted from the percolation theory taking account of the fra ctal nature of clusters. With increasing R-square beyond R*, the value of s igma ' decreases drastically as compared with that estimated from the sum o f Aslamazov-Larkin and Maki-Thompson terms. The sheet resistance dependence of sigma ' can be explained qualitatively by a model based on the scaling law of percolation. The value of T-C decreases gradually. (C) 2001 Elsevier Science B.V. All rights reserved.