Quantum vortices in type-II superconductors are known to have significant impacts on the transport properties of superconductors, thus improving the controllability of the motion of vortices has been a crucial issue. The most common method to drive vortices is the use of transport currents. In [1][2], we defined the driving force on a vortex as the sum of the magnetic and hydrodynamic forces in the framework of the time-dependent Ginzburg-Landau (TDGL) theory. We expected that the results could be extended to establish a similar picture for other driving methods, such as heat flows[3][4] and inhomogeneous spin polarization.
In [5], we investigated the dynamics of domain walls, one-dimensional topological defects, under the influence of the temperature gradient or the inhomogeneous spin polarization. The system of equations consists of the TDGL equation and the thermal / spin diffusion equation. We have shown, both analytically and numerically, that the domain walls move to the higher temperature region, where the order parameter is suppressed. This result is understood as a process reducing the loss of in the condensation energy (cf. pinning of vortices).
In this presentation, we discuss the dynamics of quantum vortices under a temperature gradient. We incorporated Ampere's law, which we did not consider in case of the dynamics of domain walls, into the system of equations.
[1] Y. Kato and C-K Chung, J. Phys. Soc. Jpn. 85, 033703/1-5 (2016).
[2] S. Sugai, N. Kurosawa and Y. Kato, Phys. Rev. B 104, 064516 (2021).
[3] M. J. Stephen, Phys. Rev. Lett, 16, 801 (1966).
[4] I. S. Veshchunov et al., Nat. Commun. 7, 12801 (2016).
[5] T. Kanakubo et al., Interplay between Domain Walls in Type-II Superconductors and Gradients of Temperature/Spin Density, arXiv:2405.10200 (2024).
Keywords: Type-II Superconductors, Vortex, Heat Flow, Ginzburg-Landau Theory