Superconducting properties in granular aluminum films near percolation threshold

Abstract

We have measured the perpendicular upper critical magnetic field H C2, the excess conductance σ ′ due to superconducting fluctuations and the superconducting transition temperature T C in granular aluminum films in the wide range of the sheet resistance R □, 100 Ω ≦R □ ≦15 k Ω. The temperature dependence of H C2 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 decreases steeply at a characteristic resistance R *≈1.5 kΩ and approaches 0.7 with increase of R □. This value of n agrees with that predicted from the percolation theory taking account of the fractal nature of clusters. With increasing R □ beyond R *, the value of σ ′ decreases drastically as compared with that estimated from the sum of Aslamazov–Larkin and Maki–Thompson terms. The sheet resistance dependence of σ ′ can be explained qualitatively by a model based on the scaling law of percolation. The value of T C decreases gradually.