Numerical Studies of Vortex Core States in Type II Superconductors

Abstract: In this thesis, we study an isolated vortex in an s-wave superconductor by solving the Bogoliubov-de Gennes equations self-consistently on a disc. We calculate the order parameter and supercurrent profiles, as well as the distribution of quasiparticle states. In contrast to quasi-classical treatments, the ratio Δ∞/EF between the order parameter and the Fermi energy is not assumed negligible. We study a regime where this ratio is on the order of 10-1, relevant to high-temperature superconductors. In this regime, we find a Friedel-like oscillation in the order parameter profile at low temperatures. This oscillation is attributed to an increased level spacing of the quasiparticle states, causing a decrease of the number of states present inside the superconducting energy gap. The results are in good agreement with previously published works. In future studies, the method used in this thesis will be generalized to d-wave superconductors.