Critical Current of Type-II Superconductors in a Broken Bose Glass State

The tilt modulus of a defective Abrikosov vortex lattice pinned by material line defects is computed using the boson analogy. It tends to infinity at long wavelength, which yields a Bose glass state that is robust to the addition of weak point-pinning centers, and which implies a restoring force per vortex line for rigid translations about mechanical equilibrium that is independent of magnetic field. It also indicates that the Bose glass state breaks into pieces along the direction of the correlated pinning centers if the latter have finite length. The critical current is predicted to crossover from two dimensional to three dimensional behavior as a function of sample thickness along the correlated pinning centers in such case. That crossover notably can occur at a film thickness that is much larger than that expected from point pins of comparable strength. The above is compared to the dependence on thickness shown by the critical current in certain films of high-temperature superconductors currently being developed for wire technology.