Vortices and vortex structures in mesoscopic and nano-superconductors

The study is an investigation of the nucleation of quantised vortices in mesoscopic superconducting discs and superconducting nanowires. Vortices nucleate in these systems when an applied magnetic fleld penetrates into the systems. A quantised vortex always carries a discrete quantum of flux. The vortex lattices in bulk samples are known to be triangular. However, in a small confined superconductor, the pattern of the vortices will be different. This is due to the fact that the effect of the boundary effect cannot be ignored in the small sample. It is interesting to understand how the presence of a boundary influences the pattern of vortices in a mesoscopic superconducting disc. To start with, we shall use London's equations. To study the systems at finite temperatures, one needs to include the entropy associated with the configuration of vortices. We also study the systems using Ginzburg-Landau equations. Recent experimental studies on Pb (lead) superconducting nanowires has found that at low temperatures far from the superconducting transition temperature, the response of the wires to a transverse applied magnetic field shows hysteresis, namely Type II response: the magnetisation curves are different under magnetic heating and cooling. Lead is a Type I superconductor and the experimental results are puzzling. The research involves a detailed numerical study of the response of Pb nanowires in applied magnetic fields at different temperatures using Ginzburg-Landau equations.