Anomalous Hall effect associated with pinning in high-κ superconductors

Abstract

Based upon the well-known normal-core model for flux lines in high-\ensuremath{\kappa} superconductors and by correctly taking into account the backflow current due to pinning forces, we analytically derived the longitudinal resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ and the Hall resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$ as functions of magnetic field in the region of flux flow. The present results qualitatively explain all the essential features of recent experiments on ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$. In particular, we demonstrate that the observed negative Hall resistivity at low magnetic field in certain high-${\mathit{T}}_{\mathit{c}}$ superconductors can be explained in terms of the existence of pinning forces in the sample.