Range and Strength of Pins Collectively Interacting with the Flux-Line Lattice in Type-ii Superconductors

Abstract

Within the theory of weak collective pinning a random pin ensemble is completely characterized by its "strength" $W$ and "range" $r_p$. We give, for the first time, a definition of $r_p$ and calculate $W$ and $r_p$ for a very general case. For point pins we find $W\sim b$ at $b\lesssim 0.3$ ($b$ is reduced induction), and $r_p=0.195a$ ($a$ is flux-line spacing) except for $b<<1\mathrm{}$ or low temperatures where $r_p\approx \mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}-\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}$. For extended pins $r_p=0.195a$ always holds but $W\left(b\right)\mathrm{}$ depends on the type and size of the pins.