Ambegaokar-Baratoff–Ginzburg-Landau crossover effects on the critical current density of granular superconductors

The critical current density of a granular superconductor, modeled as an array of Josephson-coupled grains, is calculated using a Ginzburg-Landau approach that accounts for suppression of the superconducting gap parameter in the grains by supercurrent. For a wide range of experimental parameters, the critical current density versus temperature is found to have an Ambegaokar-Baratoff dependence at low temperatures but to exhibit a crossover to a Ginzburg-Landau (1-T/$T_c$ ${)}^{3/2}$ dependence near $T_c$, the crossover occurring at the temperature for which the Josephson coupling energy of a junction is approximately equal to the superconducting condensation energy of a grain. Experimental results displaying this behavior are reported for a NbN film.