Sign reversal of the mixed-state Hall resistivity in type-II superconductors

Abstract

Taking into account pinning, thermal fluctuations, and vortex-vortex interactions, we develop a unified theory to explain the sign reversal of the mixed-state Hall resistivity ${\ensuremath{\rho}}_{\mathrm{xy}}$ in both high-${T}_{c}$ and low-${T}_{c}$ superconductors. Molecular dynamics simulations show that besides the pinning forces, either the thermal fluctuations in the high-${T}_{c}$ superconductors or the vortex-vortex interactions in the low-${T}_{c}$ ones play an important role in the sign reversal of ${\ensuremath{\rho}}_{\mathrm{xy}}.$ From a calculated phase diagram for vortex motion, we find that the abnormal Hall effect always occurs in the plastic flow state of vortices.