Motion of Vacancies in a Pinned Vortex Lattice: Origin of the Hall Anomaly

Physical arguments are presented to show that the Hall anomaly is an effect of the vortex many-body correlation rather than that of an individual vortex. Quantitatively, the characteristic energy scale in the problem, the vortex vacancy formation energy, is obtained for thin films. At low temperatures a scaling relation between the Hall and longitudinal resistivities is found, with the power depending on sample details. Near the superconducting transition temperature and for small magnetic fields the Hall conductivity is found to be proportional to the inverse of the magnetic field and to the quadratic of the difference between the measured and the transition temperatures.