Effects of quantum confinement in nanoscale superconductors: From electronic density of states to vortex matter

Due to quantum confinement, nanoscale superconductivity exhibits richer phenomena than bulk superconductivity. This will allow us to artificially design the electronic properties by changing the size and geometry of the superconductor, leading to the desired control and enhancement of superconductivity. However, the interplay between superconductivity and quantum confinement effect has not been fully understood yet. In this thesis, we theoretically investigated several aspects of nanoscale superconductivity by solving the Bogoliubov-de Gennes equations. The topics that are covered range from vortex states under the influence of quantum confinement to the electronic structure in various nano-structures. The density of states (DOS) obtained in this thesis can be compared with results from Scanning tunneling microscope (STM) experiments.;In Chapter. 3 and 4, we studied vortex states under the influence of quantum confinement effect. We found that the shape resonances of the order parameter results in an additional contribution to quantum topological confinement - leading to unconventional vortex configurations. Our results reveal a plethora of asymmetric, giant multi-vortex, and vortex-antivortex structures. They are relevant for high-Tc nanograins, confined Bose-Einstein condensates, and graphene fakes with proximity-induced superconductivity.;In Chapter. 5, we studied the effect of non-magnetic impurities in superconducting nanowires. We found that: 1) impurities strongly affect the transport properties, 2) the effect is impurity position-dependent, and 3) it exhibits opposite behavior for resonant and off-resonant wire widths due to the sub-band energy spectrum induced by lateral quantum confinement. These effects can be used to manipulate the Josephson current, filter electrons by subband.;In Chapter. 6, we investigated the Tomasch effect on the electronic structure in nanoscale superconductors. Here it is the quasiparticle interference effect induced by an inhomogeneous order parameter appearing due to quantum confinement. We found that it results in additional BCS-like Bogoliubov-quasiparticles, pseudo-gap-like structures in the DOS and modulated wave patterns in the LDOS above the superconducting gap energy. The influence of geometrical symmetry of the system is discussed.