Date of Award
Doctor of Philosophy (PhD)
Dr. J.P. Carbotte
The Eliashberg theory of superconductivity has been very successful in accounting for properties of conventional materials. The price for this success has been a lack of understanding of exactly what features of the input parameters affect the superconducting properties in significant ways. The first part of this thesis is concerned with the identification of an important parameter in the study of thermodynamic, critical magnetic field, and electromagnetic properties of a superconductor. The Bardeen-Cooper-Schreiffer (BCS) theory of superconductivity produces laws of corresponding states, i.e., various properties are predicted to have universal values. We have studied the deviations from BCS theory due to retardation effects, which are embodied in Eliashberg theory. These deviations, or corrections to BCS, can be well understood and characterized by a single simple parameter, Tc/ωln, to be defined later. Attention has been focussed on reproducing numerical (theoretical) results, since for most conventional superconducting materials, experiment agrees with theory at the 10% level.
The second half of the thesis has been largely motivated by the recent discoveries of the high-Tc oxide materials. We have applied Eliashberg-theory almost entirely in an inverse manner. That is, with little knowledge of the microscopic parameters for these new materials, we have investigated the relationships between various macroscopically observable properties, based on model spectra. The model spectra have been of three general types, the conventional category, spectra based on a combined phonon-exciton mechanism, and thirdly those based on relatively low frequency exchange bosons. We have called this latter category the very strong coupling regime. It was hoped that measured properties could uniquely specify the type of spectrum responsible for the superconductivity in the high-Tc oxides. At this point in time this goal has not really been achieved. Too many uncertainties exist in the experimental properties, a situation which has been aggravated by a lack of single crystal data. Moreover, various kinds of measurements on the same property often give very different results. At the same time the theory needs to be improved upon. For example, anisotropy ought to be incorporated into our results, since the single crystals are displaying large anisotropies. Nonetheless, some interesting signatures for the various spectral regimes have been obtained, and these are presented in the latter half of the thesis.
Marsiglio, Frank, "Eliashberg theory and the high Tc oxides" (1988). Open Access Dissertations and Theses. Paper 2109.