Date of Award
Doctor of Philosophy (PhD)
Dr. J.P. Carbotte
A 2-dimensional dx²y² symmetry superconductor is studied. The model used is a two dimensional Hubbard model with tight binding electrons in the plane with both nearest neighbor and next nearest neighbor hopping. The superconductivity is stabilized by anti-ferromagnetic spin fluctuations and is described by the Eliashberg theory.
With this model a general set of Eliashberg equations are derived which are valid for any electronic band structure and also the details of the electron-boson interaction can be included, and impurity scattering of arbitrary strength. This is possible because no model for the electronic density of states has been taken and thus all of the details of the density of states including the van Hove singularity can be accounted for fully. This leads to a non-trivial difference not previously seen between impurity scattering in the Born limit and that of impurity scattering in the unitary limit. The Eliashberg equations are solved numerically, and the effect of band structure and impurity scattering on the critical temperature is examined.
General expressions for the London penetration depth and the optical conductivity are derived. These are calculated for different impurity concentrations and scattering strengths, and band structures. It is found that the inverse square of the low temperature penetration depth is linear in temperature. This behavior can be changed to quadratic by adding small concentrations of impurity scattering in the unitary limit or by large concentrations of scattering in the Born limit. The conductivity of the normal state as well as that in the superconducting state also have a large dependence on the type of scattering included. The optical conductivity in the superconducting state shows no evidence of a gap in the spectrum in contrast to conventional superconductors. These results are compared with experimental observations on impurity doped high-Tc superconductors where similar behavior is observed.
Arberg, Peter N., "Electromagnetic Properties of 2-dimensional dx²y² Symmetry Superconductors" (1995). Open Access Dissertations and Theses. Paper 1728.