Heat capacities of granular aluminum films near the superconducting transition

The electrical conductivity and heat capacity were studied in the superconducting transition region of 1000-» thick, disordered, granular films that were evaporated onto cleaved mica substrates. The resistive transitions of films were used as thermometers in conjunction with optical heating in an ac calorimetry scheme to measure the temperature dependence of the 5 × 10^-9 J/K heat capacity of the films. Results obtained on nine samples indicated a rise in the heat capacity near the low-temperature limit of the transition region where film resistances became zero. This rise peaked in four films at values substantially greater than the estimated Bardeen-Cooper-Schrieffer jump in heat capacity and at temperatures 20-40 mK below the transition temperatures determined from a fit of the mean field theory to conductivity measurements. Quantitative comparison with theory cannot be made because transitions are broadened by film thickness variations resulting from irregular substrate topography. Results are in qualitative disagreement with the monotonic variation of the excess heat capacity calculated in the Hartree approximation. Observed peaks are also both wider and higher than those predicted by 1/n expansion and screening approximation calculations.