Date of Award
Doctor of Philosophy (PhD)
Jules P. Carbotte
Eliashberg theory, which was formulated assuming that the electron-phonon interaction is the mechanism for superconductivity, has been very successful in explaining the physical properties of most superconductors. Eliashberg theory is an extension of BCS theory, the original microscopic theory of superconductivity. BCS theory is recovered from Eliashberg theory in the weak electron-boson coupling limit. Recently, a new challenge to Eliashberg theory has been brought forth by the discovery of a new class of superconductors known as the high Tc oxides. As of this writing, the question of what is the superconducting mechanism for these materials is still unanswered. In this thesis, many superconducting properties have been calculated mainly in an effort to see if Eliashberg theory may still be applicable to these materials. The approach of this effort has depended on the property being studied. In this case of the critical temperature and the isotope effect, a great deal of work has been put in to fit actual experimental results, particularly for the isotope effect. We shall show that two distinct models, one with an additional electronic mechanism along with the phonons and the other with a very large coulomb repulsion, may be able to explain the experimental results. For the electronic specific heat, maxima that should not be exceeded by an Eliashberg superconductor are established for several quantities associated with this physical property. Unfortunately, some experimental values for these quantities appear to exceed these maxima. In the case of the the nuclear spin relaxation, which has not been very extensively studied in the past, we shall look at how the coherence peak in the relaxation rate can be reduced as a function of coupling strength and draw conclusions that are applicable to conventional superconductors. The behaviour of this property in the oxides is not ignored however, and some fitting of experiment including anisotrophy as well as antiferromagnetic Fermi liquid corrections is done. For the conductivity, we examine how one may extract the superconducting gap from this property, mainly as a theoretical exercise but inspired by the efforts of experimentalists who have tried to do this using optical data for the oxides. The low frequency conductivity, like the nuclear spin relaxation, should show a coherence peak in the BCS limit. We study this as a function of coupling strength, frequency and impurity concentration. The conductivity results here are contrasted with those obtained experimentally for the oxides. There are indications that a strong coupling mechanism may have difficulty explaining these experiments. Finally, we examine the phonon self-energy, mainly using a newly derived formula for this quantity written on the real frequency axis. Results from this new formula are compared with a previous formula written on the imaginary axis. In this case, the main concern here was theoretical and the experiments results for this quantity are only briefly touched on.
Akis, Richard, "Some applications of Eliashberg theory" (1991). Open Access Dissertations and Theses. Paper 3602.