Theory of Hall Anomaly in the Mixed State *
نویسنده
چکیده
Analogous to Peierls' arguments for the 'anomalous' Hall in metals I demonstrate that the Hall anomaly in the mixed state of superconductors, the sign change of the Hall resistivity, is a property of a vortex many-body correlation, and show that the anomaly is due to the competition between vortex vacancies and interstitials. Within this vortex many-body effect picture, many features of the complicated Hall effect can be understood in quantitative terms. For example, the expression for the vacancy formation energy is obtained, the scaling relation between the Hall and longitudinal resistivities with the power varying between 1 and 2 is found to depend on sample details, and near the superconducting 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 transition temperatures. In the past 10 years we have experienced the tremendous successes of the constructions and applications of vortex many-body theories [1], such as in the calculation of the longitudinal resistivity in the mixed state, a quantity vital for practical applications of su-perconductors. It is somehow surprising to notice that when one encounters the transverse
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