Theory of thermally activated vortex bundles flow over the directional-dependent potential barriers in type-II superocnductors

The thermally activated vortex bundle flow over the directional-dependent energy barrier in type-II superconductors is investigated. The coherent oscillation frequency and the mean direction of the random collective pinning force of the vortex bundles are evaluated by applying the random walk theorem. The thermally activated vortex bundle flow velocity is obtained.The temperature- and field-dependent Hall and longitudinal resistivities induced by the bundle flow for type-II superconducting bulk materials and thin films are calculated. All the results are in agreement with the experiments.