THEORY OF HALL ANOMALY IN THE MIXED-STATE

Analogous to Peierls' arguments for the 'anomalous' Hall in metals I d emonstrate that the Ball anomaly in the mixed state of superconductors , the sign change of the Hall resistivity, is a property of a vortex m any-body correlation, and show that the anomaly is due to the competit ion between vortex vacancies and interstitials. Within this vortex man y-body effect picture, many features of the complicated Ball effect ca n be understood in quantitative terms. For example, the expression for the vacancy formation energy is obtained, the scaling relation betwee n the Ball and longitudinal resistivities with the power varying betwe en 1 and 2 is found to depend on sample details, and near the supercon ducting transition temperature and for small magnetic fields the Hall conductivity is proportional to the inverse of the magnetic field and to the quadratic of the difference between the measured and the transi tion temperatures.