Studies in the Theory of Superconductivity.

The first part of this work is devoted to the study of superconductivity in metals having a broken-symmetry of the spin-density wave (SDW) or charge-density wave (CDW) type. Within the framework of weak coupling Bardeen-Cooper -Schrieffer (BCS) theory of superconductivity, the electron -phonon interaction and the super-conducting energy gap anisotropy are studied. Thermodynamic properties as well as tunneling properties of SIS and NIS junctions are examined. Applications of the previous results to Pb is briefly discussed. The second part contains a careful study of the pseudo-Coulomb potential in singlet superconductors. It is shown how the reduction from the screened Coulomb potential mu to the pseudo-Coulomb potential mu^* is related to the reduction of the pair correlation function of a Cooper pair at vec r = 0. In the third part, a theoretical model is developed to account for the anomalous density of states observed by scanning tunneling microscopy at the center of a vortex core in type II superconductors. The temperature and position dependence of the tunneling spectrum are predicted.