PART I. UPPER CRITICAL FIELDS AND SPAN STATES IN A-15 SUPERCONDUCTORS. PART II. VORTICES IN TWO-DIMENSIONAL SUPERCONDUCTORS

I. The upper critical fields of niobium-tin and vanadium-silicon were measured and analyzed within the Ginzburg-Landau-Abrikosov-Gor'kov theory of type II superconductivity. The importance of many-body effects on the spin states of the superconductor is stressed, especially the renormalization of the Pauli paramagnetic limiting process. For niobium-tin failure to include renormalizations from the electronphonon interaction leads to too high spin-orbit scattering rates. For a similar A15 compounds vanadium-gallium failure to include renormalizations from the electron-electron interaction (spin-fluctuations and the related Stoner factor) leads to a measured upper critical field a zero temperature which is lower than theoretically allowed. Both of these renormalizations are shown to be consistent with the existing data on the transition temperatures, heat capacities, and spin susceptibilities. In addition the upper critical fields and the transition temperatures of niobium-tin were found to be functions of the resistivities up to 60 micro-ohm centimeters, no matter if the resistivity was caused by growing niobium-tin at non-optimal temperatures, making it off-stoichiometry, or introducing third elements such as aluminum or zirconium. The upper critical field a zero temperature is maximized at 300 kilo-oersted with a resistivity of 30 micro-ohm centimeters and a transition temperature of 16 K - almost 100 kilo-oersted greater than the single crystal which has the lowest resistivity and the highest transition temperature.; II. The phase transition of Kosterlitz and Thouless, in which bound pairs of positive and negative vortices dissociate at a characteristic temperature, is shown to be possible for thin superconducting films. The resistance in the superconductor caused by this dissociation is compared to that caused by thermally activated vortices and by current-induced phase slips.