Critical currents in granular superconductors

Abstract

A relatively simple principle is experimentally demonstrated for producing extremely low critical-current density materials for application in quantum flux-flow devices. Essentially the technique consists of making the scale of structural disorder in the material small compared with the vortex core size. The smaller this ratio, the smaller the effects of bulk pinning, and the smaller the resulting critical-current density. Data for this study were obtained using superconducting granular aluminum films evaporated in a cylindrical geometry designed to eliminate edge-pinning effects. The data show $J_c$ to exhibit a sharp minimum as a function of grain size, with the lowest values of $J_c$ occurring in those films having the smallest ratio $\frac{〈D〉}{{\left({\xi }_{0}l\right)}^{\frac{1}{2}}}$. Here $〈D〉$ is the average grain size, ${\xi }_0$ is the BCS coherence length, and $l$ is the electronic mean free path. The normal-state resistivity ${\rho }_n$ can be used as an index of $\frac{〈D〉}{{\left({\xi }_{0}l\right)}^{\frac{1}{2}}}$ for the granular aluminum system, with the lowest critical-current densities occurring in films prepared to have a ${\rho }_n$ of about 10 μΩcm. In addition to discussing the dependence of the critical current on microstructure, data on the temperature dependence and electric field dependence of $J_c$ are presented.