Various topics in the theory of superconductivity

This thesis contains basically three independent but related parts. In the first part, the concept of finite compressibility of a Fermi superfluid is used to reconsider the problem of inertial mass of vortex lines in both neutral and charged superconductors at T = 0. For the charged case, in contrast to previous works where perfect screening was assumed, we take proper account of electromagnetic screening and solve exactly the bulk charge distribution caused by a moving vortex line. A similar problem for a superconducting thin film and the inertial mass for the superfluid $\sp3$He A-B interface are also considered.The second part deals with the coupling mechanisms between vortex pancakes in neighboring superconducting thin films. We have discovered that in addition to the well known Josephson coupling and Ampere coupling, there is a new coupling mechanism due to virtual Coulomb interaction. In contrast to the former two mechanisms, this Coulomb coupling tends to dissociate a vortex line. At least in high-T$\sb{\rm c}$ Bi-materials and in many superconductor-insulator superlattices this new mechanism may be important.The last part examines the viability of the "Efetov-Larkin" state (s-wave, spin triplet, odd between layers) as an identification of the pairing state of those cuprate superconductors which contain double CuO$\sb2$ planes. It is concluded that most of the NMR and other data are consistent with this assignment but there are one or two obvious difficulties.U of I OnlyETDs are only available to UIUC Users without author permissio