Spin Hall effect generated by fluctuating vortices in type-II superconductors.

We theoretically investigate the vortex spin Hall effect, i.e., a novel spin Hall effect driven by the motion of superconducting vortices, by focusing on the role of superconducting fluctuations. Within the BCS-Gor'kov microscopic approach combined with the Kubo formula, we find a strong similarity between the vortex spin Hall effect and the vortex Nernst/Ettingshausen effect. Calculated temperature dependence of the voltage signal due to the inverse vortex spin Hall effect exhibits a strong enhancement by vortex fluctuations. This result not only provides a possible explanation for a prominent peak found in the spin Seebeck effect in a NbN/Y$_3$Fe$_5$O$_{12}$ system, but also leads to a proposal of new experiments using other superconductors with strong fluctuations, such as cuprate or iron-based superconductors.