The influence of the Hall force on the vortex dynamics in type II superconductors

The effect of the Hall force on the pinning of vortices in type II superconductors is considered. A field theoretic formulation of the pinning problem allows a non-perturbative treatment of the influence of quenched disorder. A self-consistent theory is constructed using the diagrammatic functional method for the effective action, and an expression for the pinning force for independent vortices as well as vortex lattices is obtained. We find that the pinning force for a single vortex is suppressed by the Hall force at low temperatures while it is increased at high temperatures. The effect of the Hall force is more pronounced on a single vortex than on a vortex lattice. The results of the self-consistent theory are shown to be in good agreement with numerical simulations.