Origin of Hall Anomaly in the Mixed State

There has been a corporative absence of understanding of Hall anomaly data in the mixed state in terms of vortex many-body effect and pinning, because of the dominant theoretical influence. Now D'Anna et al. [ Phys. Rev. (cond-mat/9808164)] are brave enough to announce the prominent role played by vortex many-body effect and pinning in their interpretation of their own data. Here I wish to point out: (1) Indeed the data of D'Anna et al. can be explained within an existing Hall anomaly theory based on vortex many-body considerations; (2) It is not surprising that their data are not consistent with available microscopic Hall anomaly theories, because those theories are mathematically incorrect; and (3) The courage of D'Anna et al. should be appreciated. The clear correlation between the Hall anomaly and the vortex many-body effect reported first by D'Anna et al. [1] has not only put all previous independent vortex theories into question, also required a drastic change in the interpretation of the relevant data, where the vortex many-body effect has been consistently absent, because of the dominant theoretical influence. The purpose of this Comment is to sharpen this situation by pointing out: (1). Indeed an existing vortex many-body theory for the Hall anomaly is consistent 1 with the observation of D'Anna et al.; and (2). Several independent vortex dynamical theories are mathematically incorrect. Generally, it has been known that independent particle models, Drude type models, cannot give a proper explanation of the Hall effect in a solid [2], and that the Hall effect is a result of the interplay between the many-body effect arising from Fermi statistics and electron-electron interaction and a background potential, periodic or random. For the Hall anomaly in the mixed