Characteristic Parameters of a Granular Superconductor

Starting from a simple microscopic model of a granular superconductor (cubic grains of superconductor weakly coupled by Josephson junctions separating adjacent cubes), a calculation is made of the characteristic parameters $\mathfrak{J}$ and $C$ of the continuum model of a granular superconductor, $\mathfrak{J}$ being the proportionality constant of the tunneling energy, and $C$ the proportionality constant of the electrostatic energy density. From these are calculated the characteristic frequency $\omega$ for the onset of electromagnetic oscillations, the characteristic length $\xi$, the Ginzburg-Landau coherence distance ${\xi }_{\mathrm{GL}}$, and the magnetic penetration depth $\lambda$. The last two are identical with the corresponding quantities for a dirty superconductor in the vicinity of the superconducting transition temperature. In the limit of weak magnetic fields, the identity of $\lambda$ holds for all temperatures.