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<p>We study Ginzburg–Landau equations for a complex vector order parameter to a two-component system. We discuss the existence, uniqueness, asymptotics, monotonicity and stability of solutions by extending Alama-Bronsard-Mironescu's results in a more general case.</p> / Doctor of Philosophy (PhD)

The topological aspects of superconductivity on doped Weyl semimetals are investigated. / Topological phases of matter have sparked significant experimental and theoretical interest due to the topologically robust edge modes they host, as well as their classification through rich mathematics. An interesting example of a topological phase in three dimensions, the Weyl semimetal, can exhibit topological ordering through the existence of Fermi arcs on the surfaces of the material. For the doped Weyl semimetal, we investigate possible resulting Weyl superconducting states --- both the inter-Fermi surface pairing state following Li and Haldane, and the intra-Fermi surface pairing state following Burkov --- in this thesis, and study their topological properties by computing the gapless Weyl-Majorana edge modes they host. The results obtained in Ref. \cite{LH} for the inter-Fermi surface superconducting state are reproduced, and the bulk and edge properties of the intra-Fermi surface pairing superconducting state are studied in detail. / Thesis / Master of Science (MSc) / In this thesis, we study an interesting class of topological materials called the Weyl semimetal as well as its associated superconducting phases. A description of the Fermi arcs on Weyl semimetals are given, and the topological properties of the inter-Fermi surface and intra-Fermi surface pairing states are studied in detail.

Enhanced field emission (EFE) presents the main impediment to higher acceleration gradients in superconducting niobium (Nb) radiofrequency cavities for particle accelerators. The strength, number and sources of EFE sites strongly depend on surface preparation and handling. The main objective of this thesis project is to systematically investigate the sources of EFE from Nb, to evaluate the best available surface preparation techniques with respect to resulting field emission, and to establish an optimized process to minimize or eliminate EFE. To achieve these goals, a scanning field emission microscope (SFEM) was designed and built as an extension to an existing commercial scanning electron microscope (SEM). In the SFEM chamber of ultra high vacuum, a sample is moved laterally in a raster pattern under a high voltage anode tip for EFE detection and localization. The sample is then transferred under vacuum to the SEM chamber equipped with an energy-dispersive x-ray spectrometer for individual emitting site characterization. Compared to other systems built for similar purposes, this apparatus has low cost and maintenance, high operational flexibility, considerably bigger scan area, as well as reliable performance. EFE sources from planar Nb have been studied after various surface preparation, including chemical etching and electropolishing, combined with ultrasonic or high-pressure water rinse. Emitters have been identified, analyzed and the preparation process has been examined and improved based on EFE results. As a result, field-emission-free or near field-emission-free surfaces at ~140 MV/m have been consistently achieved with the above techniques. Characterization on the remaining emitters leads to the conclusion that no evidence of intrinsic emitters, i.e., no fundamental electric field limit induced by EFE, has been observed up to ~140 MV/m. Chemically etched and electropolished Nb are compared and no significant difference is observed up to ~140 MV/m. To address concerns on the effect of natural air drying process on EFE, a comparative study was conducted on Nb and the results showed insignificant difference under the experimental conditions. Nb thin films deposited on Cu present a possible alternative to bulk Nb in superconducting cavities. The EFE performance of a preliminary energetically deposited Nb thin film sample are presented. / Ph. D.

This work is concerned with the formulation and analysis of a simplified GinzburgLandau type model of superconductivity which is valid for large K and large magnetic field strengths. This model, referred to as the High kappa model, is derived via formal asymptotic expansion of the full, time-dependent Ginzburg-Landau equations. The model accounts for the effects of both applied magnetic fields and currents of constant magnitude. A notable feature of our model is that the systems for the leading order terms for the magnetic potential and the order parameter are decoupled. Finite element approximations of the High kappa model are introduced using standard Galerkin discretization in space and Backward-Euler and Crank-Nicolson discretization schemes in time. We establish existence and uniqueness results for the fully-discrete equations as well as optimal L2 and HI error estimates for the Backward-Euler-Galerkin and the Crank-Nicolson-Galerkin problems. Computational experiments are performed with several combinations of spatial and time discretizations of the High kappa model equations. Among other things our numerical approximations show good agreement for rates of convergence in space and time with the corresponding theoretical values. Finally, some well known steady-state and dynamic phenomena valid for type II superconductors are illustrated numerically. / Ph. D.

The properties of superconducting lead have been studied using the technique of electron tunnelling through a thin insulating barrier. Certain features in the second derivative of the current voltage characteristic of this tunnelling mechanism have been related to the phonon spectrum of lead. In addition, a small amount of bismuth impurities have been added and the effect of these impurities on the superconducting density of states reported. In particular, both the superconducting energy gap has widened and the phonon spectrum of lead altered with the addition of these impurities. / Thesis / Master of Science (MS)

This thesis investigates the impacts of superconducting magnetic energy storage (SMES) unit on the power system first-swing stability by the impedance model of the SMES unit and EMTP simulations. The impedance model of the SMES unit is established in this thesis for study purpose. It has been concluded that SMES unit can greatly improve the power system first-swing stability. Based on the theoretical analysis and simulation results, the concept of the "Stability Protection Zone" of the SMES unit is proposed. Future work directions are discussed in the conclusion part. / Master of Science