The effects of quantum and thermal fluctuations on collective pinning and critical current density Jc are investigated for bulk type-II superconductors by utilizing quantum statistics. It is shown that for a constant magnetic field, Jc is nearly independent of temperature in the quantum limit; however, in the classical limit, Jc decreases weakly with increasing temperature when T < Tdp (depinning temperature); when Tdp < T < Tf (boundary fluctuation temperature), Jc is power-law-decaying, and when T > Tf, Jc decays exponentially. For constant temperature, Jc first decreases, then increases after reaching a maximum, and finally decreases again. These results are in agreement with the experiments.
Collective pinning of imperfect vortex lattices by material line defects in extreme type-II superconductors