Pinning by the local changes of the electron mean free path in anisotropic type-II superconductors

The bulk pinning force density $F_p$ and the critical current $j_c$ of a dirty type-II superconductor, with spatially varying electron mean free path l along a given direction, are calculated using the Ginzburg-Landau-Abrikosov theory. In high fields the critical force density $F_c$ is proportional to (1-B/$B_{c2}$ ${)}^2$(B/$B_{c2}$ ${)}^m$, where 0<m<1, but depends also on the size and form of inhomogeneity (grain boundary, dislocation wall, etc.) which causes the change of l. This may explain deviations from straight lines in the ‘‘Kramer plots’’ of $j_c^{1/2}$ $B^{1/4}$ versus B/$B_{c2}$ and the approximate scaling of $F_c$ when the temperature is changed.