Heat-Capacity Measurements of the Critical Coupling between Aluminum Grains

We have measured the heat capacity of granular aluminum specimens with normal-state resistivities ${\rho }_N$ between 0.6×${10}^{-3\mathrm{}}$ and 40 × ${10}^{-3\mathrm{}}$ Ω cm. The specimens become superconducting with a heat-capacity transition which is BCS-like for the lowest ${\rho }_N$, and then diminishes until it is no longer observable for the highest ${\rho }_N$. We conclude that the grains become decoupled such that, because of their small size, they do not exhibit bulk superconductivity when they are isolated.