Directional-dependent thermally activated motion of vortex bundles and theory of anomalous Hall effect in type-II conventional and high-Tc superconductors

The anomalous Hall effect for type-II conventional and high-Tc superconductors is studied based upon the theory of thermally activated motion of vortex bundles jumping over the directional-dependent energy barrier. It is shown that the Hall anomaly is universal for type-II conventional and high-Tc superconductors as well as for superconducting bulk materials and thin films, provided certain conditions are satisfied. We find that the directional-dependent potential barrier of the vortex bundles renormalizes the Hall and longitudinal resistivities, and Hall anomaly for superconductors is induced by the competition between the Magnus force and the random collective pinning force of the vortex bundle. We also find that the domain of anomalous Hall effect includes two regions: the region of thermally activated motion of the small vortex bundles and that of the large vortex bundles separated by the contour of the quasiorder-disorder first-order phase transition, or the peak effect of the vortex system. The Hall and longitudinal resistivities as functions of temperature as well as applied magnetic field have been calculated for type-II superconducting films and bulk materials. The conditions for occurring the double sign reversal or reentry phenomenon is also investigated. All the results are in agreement with the experiments.