Fluctuation Spectroscopy in Granular Superconductors with Application to Boron-doped Nanocrystalline Diamond

We perform a detailed calculation of the various contributions to the fluctuation conductivity of a granular metal close to its superconducting transition. We find three distinct regions of power law behavior in reduced temperature, $\eta=(T-T_c)/T_c$, with crossovers at $\Gamma/T_c$ and $E_{Th}/T_c$, where $\Gamma$ is the electron tunneling rate, and $E_{Th}$ is the Thouless energy of a grain. The calculation includes both intergrain and intragrain degrees of freedom. This complete theory of the fluctuation region in granular superconductors is then compared to experimental results from boron-doped nanocrystalline diamond, using the assumption of a constant phase breaking rate, $\tau_{\phi}^{-1}$. We find a semi-quantitative agreement between the theoretical and experimental results only in the case of large phase breaking. We argue that there may be a novel phase breaking mechanism in granular metals worthy of further experimental and theoretical investigation.