Guiding of vortices and the Hall conductivity scaling in a bianisotropic planar pinning potential

Abstract

The exactly solvable stochastic planar model of anisotropic pinning of vortices by two different orthogonally oriented washboard potentials at the temperature $T>~0$ and at arbitrary values of the vortex viscosity $\ensuremath{\eta}$ and the Hall constant ${\ensuremath{\alpha}}_{H}$ is considered. The model describes nonlinear anisotropy effects caused, e.g., by the coexistence of intrinsic and twin-plane or grain-boundary pinning in layered high-${T}_{c}$ superconductors. Nonlinear guiding effects are discussed and the critical current anisotropy is analyzed. New anisotropic scaling relations for the Hall conductivity are predicted and the interrelation between the guiding of vortices and the Hall effect in nonlinear regimes is considered.