Heat-Capacity Measurements of the Critical Coupling between Aluminum Grains

Abstract

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