Guiding of Vortices and the Hall Effect in Superconductors with Unidirected Twins

Unidirected twin planes are the cause of anisotropic pinning of vortices in YBa₂Cu₃O_7-δ single crystals. In contrast to the case of only isotropic pinning, two new effects may appear due to the pinning anisotropy: guiding of vortices along twin planes and anisotropy of the Hall resistivity. The former leads to the appearance of the even (with respect to the reversal of a magnetic field direction) transverse resistivity and influences the Hall angle, while the last causes new additional odd contribution to the longitudinal resistivity. In the presence of anisotropic and isotropic pinning the nonlinear vortex dynamics is theoretically discussed in terms of phenomenologically introduced anisotropic drag and pinning viscosities. Experimental reconstruction of those viscosities is proposed on the basis of formulas for four experimentally observed nonlinear longitudinal and transverse magnetoresistivities (odd and even with respect to the magnetic field reversal). Assuming the anisotropic pinning alone: a) new scaling relations for the anisotropic Hall conductivity are predicted; b) nonlinear guiding effects are discussed; c) specific current and angular behavior of current-voltage characteristics is analyzed. We also explicitly investigate the nonlinear vortex dynamics in twinned superconductors on the basis of the two-dimensional Fokker-Planck equation. New current- and angle-dependent guiding effects, scaling of the anisotropic Hall conductivity and temperature-dependent behavior of the longitudinal and transverse magnetoresistivity are presented. The comparison of the two approaches (phenomenological and stochastic) is made. The phe-nomenological formulas for linear galvanothermomagnetic effects are derived and analyzed under condition at which the transport current or thermal gradient is directed at arbitary angle with respect to the unidirected twins. We show that new additional odd contribution to longitudinal resistivity might be masked in the experiment by a large, odd contribution, which has the same angular dependence and which appears due to the Ettingshausen effect. In order to clarify the problem of influence of the twins on the Hall drag coefficient, we discuss the possibility of separating these two new contributions in the experiment. A review of recent experimental observations of guiding of vortices and the anisotropic Hall conductivity in YBa₂Cu₃O_7-δ single crystals with unidirected twins also is given and several new experiments in the field are proposed.