Theory of flux motion with backflow current in high-κ superconductors

Based upon the well-known normal-core model for flux line in high-κ superconductors and by correctly taking into account the backflow current due to both pinning forces and other vortices, we developed a theory for flux motion in the framework of the Bardeen-Stephen and Nozières-Vinen approaches. We derived analytically the longitudinal resistivity ${\mathrm{\rho }}_{\mathit{x}\mathit{x}}$ and the Hall resistivity ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$ as functions of the magnetic field in the region of flux flow. Our results explain qualitatively all the essential features of recent experiments on ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$, including, in particular, the observed negative Hall resistivity at low magnetic field in certain high-${\mathit{T}}_{\mathit{c}}$ superconductors. Furthermore, a long-standing problem concerning the expressions for the viscous-drag force and the applied force on a vortex is discussed and clarified.