M.Sc. Physicshttp://hdl.handle.net/10464/22502015-01-28T01:22:08Z2015-01-28T01:22:08ZPlanar Topological Defects in Unconventional SuperconductorsPrzedborski, Michellehttp://hdl.handle.net/10464/49872013-10-03T06:00:54Z2013-09-12T00:00:00ZPlanar Topological Defects in Unconventional Superconductors
Przedborski, Michelle
In this work, we consider the properties of planar topological defects in unconventional
superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper-
Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors
with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.
2013-09-12T00:00:00ZInfrared Spectroscopy of GadoliniumObied, Lailahttp://hdl.handle.net/10464/42752013-10-16T13:04:52Z2013-04-10T00:00:00ZInfrared Spectroscopy of Gadolinium
Obied, Laila
Measurements of the optical reflectivity of the normal incident light along c-axis [0001]
have been made on a Gadolinium single crystal, for temperatures between 50 K and
room temperature just above the Curie temperature of Gd, which is 293 K. And
covering the spectrum range between 100 -11000 cm-I . This work is the first study
of Gd in the far infrared range. In fact it fills the gap below 0.2 eV which has never
been measured before.
Extreme attention was paid to the fact that Gadolinium is a very reactive metal
with air. Thus, the sample was mechanically polished and carefully handled during
the measurement. However, temperature dependent optical measurements have been
made in the same frequency range for a sample of Gd2O3. For comparison, both
samples of Gd and Gd2O3 were examined by X-Ray diffraction. XRD analysis showed
that the sample was pure gadolinium and the oxide layer either does not exist, or is
very thin. Furthermore, this fact was supported by the absence of any of Gd2O3
features in the Gd sample reflectivity.
Kramers Kronig analysis was applied to extract the optical functions from the
reflectance data. The optical conductivity shows a strong temperature dependence
feature in the mid-infrared. This feature disappears completely at room temperature
which supports a magnetic origin.
2013-04-10T00:00:00ZOptical Properties of Sb2Te3, and Dilute Magnetic Semiconductors Sb1.97 VO.03 Te3 and Sb1.94 CrO.06 Te3Manson, Jasonhttp://hdl.handle.net/10464/42642013-10-16T13:23:21Z2013-04-09T00:00:00ZOptical Properties of Sb2Te3, and Dilute Magnetic Semiconductors Sb1.97 VO.03 Te3 and Sb1.94 CrO.06 Te3
Manson, Jason
This thesis reports on the optical properties of the dilute magnetic semiconductors, Sb1.97 V 0.03 Te3 and Sb1.94Cr0.06Te3, along with the parent compound Sb2Te3' These materials develop a ferromagnetic state at low temperature with Curie temperatures of 22 K and 16 K respectively. All three samples were oriented such that the electric field vector of the light was perpendicular to the c-axis. The reflectance profile of these samples in the mid-infrared (500 to 3000 cm-1) shows a pronounced plasma edge which retracts with decreasing temperature. The far-infrared region of these samples
exhibits a phonon at ~ 60 cm-1 which softens as temperature decreases. Kramers-Kronig analysis and a Drude-Lorentz model were employed to determine the optical constants of the bulk samples. The real part of the optical conductivity is shown to consist of intraband contributions at frequencies below the energy gap (~0.26 eV) and interband contributions at frequencies above the energy gap. The temperature dependence of the scattering rate show that a mix of phonon and impurity scattering are present, while the signature of traditional spin disorder (magnetic) scattering was difficult to confirm.
2013-04-09T00:00:00ZGeneralization of the BTK Theory to the Case of Finite Quasiparticle LifetimesRohanizadegan, Yousefhttp://hdl.handle.net/10464/41852013-10-02T20:07:37Z2013-01-24T00:00:00ZGeneralization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes
Rohanizadegan, Yousef
A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy.
The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.
2013-01-24T00:00:00Z