Dynamics of Topological Defects in Type-II Superconductors under Gradients of Temperature/Spin Density

Abstract

We theoretically investigate the motion of a domain wall and a vortex in type-II superconductors driven by inhomogeneities of temperature or spin accumulation. The model consists of the time-dependent Ginzburg-Landau equation and the thermal or spin diffusion equation, whose transport coefficients, such as the thermal and spin conductivities and the spin relaxation time, depend on the order parameter and interpolate between their values in the superconducting and normal states. Numerical and analytical calculations indicate that the domain wall moves toward the higher-temperature region or the region with larger spin accumulation, where the order parameter is suppressed. We also derive analytical expressions for the vortex velocity and confirm the predicted direction of vortex motion by numerical simulations. The dynamics of these topological defects can be understood as processes that reduce the loss of condensation energy. We also analyze the driving force, viscous force, thermal force, and force due to the spin accumulation gradient on the basis of momentum balance relations.