Abstract: The nonreciprocal charge transport property which depends on the polarity of the applied current, such as the diode effect and the rectification effect, is of great importance for both theoretical research and engineering application. The nonreciprocal transport property in superconductors generally requires to break both the spatial inversion symmetry and the time-reversal symmetry, and therefore becomes one of the fundamental issues in superconductivity. Of particular interest, the superconducting diode effect, which exhibits one-way superconductivity, can potentially be applied to dissipationless diode devices, as a consequence has received extensive attention in recent years. In this Ph. D thesis, we simulate vortex dynamics with heat dissipation by numerically solving time-dependent Ginzburg-Landau equations and heat transfer equation. The nonreciprocal transport properties of the following three superconducting systems are studied. We study a superconducting film patterned with a conformal pinning array and find a giant rectification effect which is consistent with the experimental observation. In presence of the funneling effect due to the geometry of the conformal pinning array, Joule heating of the accumulating vortices creates hot spots and drives the sample to the normal state. Meanwhile, the density gradient of vortex does not match the gradient of pinning. The two mechanisms together lead to the giant rectification effect. We study the nonreciprocal charge transport property in a pinning-free superconducting nano-ring. We systematically calculate the response of the ratchet signal to various parameters in both D.C. and A.C. currents. By analyzing the vortex potential, we find that the nonreciprocal transport property is caused by the asymmetry potential barriers for vortex entry and exit. We study a superconductor/nanoscale-magnetic-dot hybrid structure. It takes advantage of the external current to control the nucleation of vortex-antivortex pairs, and can produce superconducting diode effect without applied magnetic fields. Our vortex dynamics simulation details the progress of the superconducting-normal phase transition due to motion of vortex pairs and heat dissipation. The nonreciprocal transport properties of the above three systems are all based on the broken symmetry of spatial inversion, which is caused by the anisotropic pinning array, the asymmetric geometry, and the nonuniform distribution of the magnetic field, respectively. The mechanisms we discuss in this thesis do not require special property of the materials and thus can be applied to any kinds of conventional superconductors. The present studies would provide solid theoretical basis for the future design and application of the dissipationless superconducting devices.

Abstract: Responses of mesoscopic superconducting rings and disks to perpendicular magnetic fields are studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the sample are measured simultaneously. This allows us for a direct experimental observation of the paramagnetic supercurrent, which is closely related to the paramagnetic Meissner effect. The results are compared with numerical results based on the nonlinear Ginzburg-Landau theory.