Date of Award
Doctor of Philosophy (PhD)
Jules P. Carbotte
Within the context of Eliashberg theory, we have studied the effects
of planar anisotropy on many superconducting properties. Planar anisotropy
is of interest for superconductors with layered crystal structure, such as the
metallic transition metal dichalcogenide and high-Tc oxide superconductors.
To describe planar anisotropy we use a model dispersion relation
which gives free-particle-like electronic states in the direction parallel to the
layers and the tight-binding form in the direction perpendicular to the layers.
Using this dispersion relation and the Fermi-Surface-Harmonic (FSH)
expansion technique, we specify the general anisotropic Eliashberg equations
for the problem of planar anisotropy.
We begin with the study of the effects of planar anisotropy on the superconducting
transition temperature, the thermodynamic critical magnetic field, and the quasiparticle density of states in the superconducting state. For all these properties, especially the quasiparticle density of states, the effects
of planar anisotropy are usually qnite significant.
Next, we study some thermodynamic and transport properties, namely,
the specific heat, the thermal conductivity, and the ultrasound attenuation.
The effects of planar anisotropy on these properties are closely related to the
changes in the quasiparticle density of states due to anisotropy. The changes
in the quasiparticle lifetime due to the superconducting phase transition and
anisotropy are also important for the unusual behaviors of thermal conductivity
at low temperature.
Several electromagnetic properties are also studied. The introduction of anisotropy usually reduces the value of the London penetration depth below its isotropic value, and strongly depresses the Hebel-Slichter peak in the nuclear spin relaxation rate. The theorerical results for the nuclear spin relaxation rate with strong coupling, anisotropy and Fermi liquid corrections have been compared with the experimental data for the high-Tc oxides. The
major effect of planar anisotropy on the infrared conductivity is to reduce
the frequency at which the absorption starts.
Finally, we have examined the changes of the phonon self-energy when the superconducting phase transition occurs. It is found that there
is a qualitative difference between the results for isotropic superconductors
and for anisotropic ones. This may be displayed in experiment under certain
conditions. Anisotropy also complicates the analysis of the structures in the
It is generally true, for all the properties which we have studied,
that the effects of anisotropy will be diminished if we increase the coupling
strengths, and/or introduce impurity scatterings.
Besides the problem of planar anisotropy, we briefly discuss the problem
of an energy dependent electronic density of states (EDOS) for Eliashberg
superconductors. This is of interest for a model of two-dimensional
tight-binding dispersion relation. For a Lorentzian form for EDOS around the
Fermi level, we have discussed the modifications of the Eliashberg equations
and, then, calculated the quasiparticle density of states in the superconducting
state. The effects of an energy dependent electronic density of states on
the temperature evolution of the quasiparticle density of states below Tc is
Jiang, Chao, "Effects of Planar Anisotropy on Eliashberg Superconductors" (1992). Open Access Dissertations and Theses. Paper 3946.