Theory of anomalous Hall effect for type-II high-Tc and conventional superconductors

The anomalous Hall effect for type-II superconductors is investigated by random walk theorem. It is shown that the origin of Hall anomaly is induced by the thermally activated vortex bundle flow (TAVBF) over the directional-dependent energy barrier formed by the Magus force, random collective pinning force, and strong pinning force inside the vortex bundles. The directional-dependent potential barrier of the vortex bundles renormalizes the Hall and longitudinal resistivities strongly. Under the framework of present theory, it is also shown that the Hall anomaly is universal for type-II superconductors, either high- or conventional as well as bulk materials or thin films. The conditions for Hall anomaly and reentry phenomenon are derived, the Hall and longitudinal resistivities as well as Hall angle for type-II superconducting films and bulk materials versus temperature and applied magnetic field are calculated. All the results are in agreement with the experiments.