| In order to understand the complex electromagnetic properties of high temperature superconductors the details of the electronic band structure must be included. In this thesis we go beyond the simple free electron model in which the electromagnetic properties are determined by a single, spherical, Fermi surface (which is adequate for most conventional superconductors) to more realistic models containing multiple, anisotropic tight binding bands. Using these models we are able to calculate several electromagnetic properties, including the magnetic penetration depth, Josephson tunneling currents, the density of states and the optical conductivity, we find our results are in good agreement with experimental observations.; One of the banes of the field of high temperature superconductivity is that many experiments are carried out on materials that are less than ideal. Often the presence of impurities or less than ideal stoichiometries can have a large impact upon the measured properties. We are able to calculate the effect of impurities upon the above mentioned electromagnetic properties in both the unitary and Born scattering limits and find significant differences between them. We find that the presence of impurities in the chain band has little effect upon the critical temperature which is consistent with the experimental observations that Ni impurities (which go into the chains) and overdoped materials (in which the excess oxygen also goes in the chains) have little effect upon the critical temperature, while Zn impurities (which go into both the chains and planes) and underdoped materials (in which both the chains and planes are oxygen deficient) have a significantly lower critical temperature.; Another of the difficulties with the experimental results is caused by the presence of twin domains in the orthorhombic materials. The presence of twins in a material can mask some of the significant anisotropies that are observed in untwinned materials such as the magnetic penetration depth in the a and b directions and the c direction Josephson tunneling into a conventional superconductor. We calculate these properties in models that take into account the large anisotropies that are present in these materials. We find that the c direction Josephson tunneling can not only be non-zero, but can actually be quite large in a pure d wave superconductor if the band is anisotropic (i.e. orthorhombic). This result helps explain one of the few experiments that was considered inconsistent with d wave superconductivity. |
