Dynamics of vortices in planar pinning centers and anisotropic conductivity in type-II superconductors

Abstract

We investigate the two-dimensional dynamics of vortices in planar pinning centers with thermal fluctuations on the basis of a Fokker-Planck equation and derive explicit expressions for the electric conductivity tensor σij and the resistivity tensor ρij due to the vortex motion. It is shown that the off-diagonal components σxy and ρxy have large symmetric contributions, which do not change their signs upon reversing the magnetic-field direction due to the anisotropy of pinning and of vortex viscosity. The symmetric part of the transverse resistivity, referred to as the even Hall effect, arises from competition between the guided motion of vortices in planar pinning centers and the thermal hopping of vortices over the pinning barriers. A scaling law for a current parallel to the pinning planes is expected as ρ⊥∝ρ‖, where ρ⊥ is the transverse resistivity and ρ‖ is the longitudinal resistivity.

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