The Confinement of Vortices in Nano-Superconducting Devices

We have investigated the confinement of 3-D vortices in specific cases of Type-II ($\kappa = 2$) nano-superconducting devices. The emergent pattern of vortices greatly depends on the orientation of an applied magnetic field (transverse or longitudinal), and the size of the devices (a few coherence lengths $\xi$). Herein, cylindrical geometries are examined. The surface barriers become very significant in these nano-systems, and hence the characteristics of the vortices become highly sensitive to the shape of the system and direction of an applied field. It is observed that nano-cylindrical superconductors, depending on their sizes, can display either first or second order phase transitions, under the influence of a longitudinal field. In the confined geometries, nucleation of a giant vortex state composed of a n-quanta emerges for the longitudinal magnetic field.