Effects of quantum and thermal fluctuations on collective pinning and critical current density in type-II superconducting bulk materials

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