Size Effect in a Granular Superconductor

The superconducting energy gap and the transition temperature of a small grain of superconductor are larger than the corresponding quantities for bulk material. This results because the small dimensions cause a discrete, rather than continuous, spectrum of one-electron energy levels. This effect becomes important when the volume of the grain is comparable with, or smaller than, the characteristic volume ${{\lambda }_F}^2{\xi }_0$, where ${\lambda }_F$ is the Fermi wavelength and ${\xi }_0$ the $T=0\mathrm{}$ Pippard coherence distance of the bulk material. As grain size is lowered, the ratio of $T=0\mathrm{}$ energy gap to Boltzmann's constant times transition temperature gradually increases from the weak-coupling limit (3.528) to the strong-coupling limit (4.0).