  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.
