Nonlinear generalization of the Bardeen-Stephen model and the Hall angle anomaly

Abstract

The two classical models for the moving vortex, one suggested by Bardeen and Stephen ͑BS͒ and the other by Noziéres and Vinen ͑NV͒, are incompatible regarding the nature of normal core current upon which the dissipation characteristics depend. In order to resolve this ambiguity, we generalize the BS model by including the nonlinear convection term. This nonlinear generalization leads to an additional electric field inside and outside the core which was not accounted for in the BS model. The electric force field in the core is found to be identical to the NV model. Using this field, we determine the normal core current and the rate of energy dissipation in the core. The rate of energy dissipation allows us to determine the drag coefficients proposed by Hagen et al. From these coefficients, we demonstrate the appearance of the negative Hall angle if the effective pinning force is small compared to the Lorentz force.