Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Professor Jules Carbotte


We utilize Eliashberg theory, up to the Migdal approximation, to study some properties of two dimensional superconductors. The mechanism of superconductiviiy in this thesis is bosonic, either caused by phonons or by spin fluctuations. The order parameter is an s-wave for the phonon mechanism or a d-wave when considering spin fluctuations.

The two dimensional (2D) superconductor is modeled by a stack of conducting sheets and coupling between the sheets is neglected for simplicity. The electronic density of states (EDOS) of a 2D electron gas on a lattice possesses a singular peak usually called a van Hove singularity (vHs). The presence of a vHs near the Fermi level is shown to enhance the superconducting transition temperature, Tc, for both mechanisms as well as reduce the isotope effect, β, from its standard value of 0.5 (predicted by BCS theory).

The Eliashberg equations (EE) on the imaginary axis are handled in two ways i) the EDOS is used directly when integrating out the energy dependence of the EE to get analytical expressions that can be solved numerically ii) the k-sum is handled numerically from the start and the whole 2D Brillouin zone is used. In the first approach, infinite band models of EDOS are used, in the second only the dispersion of the electron gas has to be specified.

Some of the properties calculated in this thesis are the critical temperature, the isotope effect (for phonons only), the specific heat difference and its jump at Tc, the thermodynamic critical field, the upper critical field and the London penetration depth. Impurity scattering is also considered, in Born approximation and in resonance scattering (for d-wave only). Experimental comparison with our results show that the isotope effect and the specific heat jump at Tc correlate very well with an s-wave order parameter, while the low temperature dependence of the London penetration depth and some superconducting specific heat results are best described by a d-wave order parameter.

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